A local manufacturing firm produces four different metal products, each of
which must be machined, polished and assembled. The specific time
requirements (in hours) for each product are as follows:

The firm has available to it on weekly basis, 480 hours of machining time, 400 hours of polishing time and 400 hours of assembling time. The unit profits on the product are Birr 360, Birr 240, Birr 360 and Birr 480, respectively.The firm has a contract with a distributor to provide 50 units of product I, and 100 units of any combination of products II and III each week. Through other customers the firm can sell each week as many units of products I, II and III as it can produce, but only a maximum of 25 units of product IV. How many units of each product should the firm manufacture each week to meet all contractual obligations and maximize its total profit? Make a mathematical model for the given problem. Assume that any unfinished pieces can be finished the following week.

Answers

Answer 1

Step-by-step explanation:

The firm should manufacture 50 units of product I, 100 units of product II, and 100 units of product III each week to meet all contractual obligations and maximize its total profit.

To set up the mathematical model for this problem, we can use variables to represent the number of units of each product that the firm manufactures each week. Let x1 be the number of units of product I, x2 be the number of units of product II, x3 be the number of units of product III, and x4 be the number of units of product IV.

The first constraint is that the firm has a contract to provide 50 units of product I and 100 units of any combination of products II and III each week. This can be represented as:

x1 = 50

x2 + x3 = 100

The second constraint is that the firm has a maximum of 480 hours of machining time, 400 hours of polishing time, and 400 hours of assembling time each week. The time required for each product can be represented as:

x16 + x28 + x34 + x410 <= 480 (machining time)

x14 + x26 + x32 + x48 <= 400 (polishing time)

x14 + x24 + x34 + x46 <= 400 (assembling time)

The third constraint is that the firm can sell as many units of products I, II, and III as it can produce, but only a maximum of 25 units of product IV. This can be represented as:

x1 >= 0

x2 >= 0

x3 >= 0

x4 <= 25

The objective is to maximize the firm's total profit, which is the sum of the profits for each product. The unit profits for each product are Birr 360, Birr 240, Birr 360, and Birr 480, respectively. The total profit can be represented as:

360x1 + 240x2 + 360x3 + 480x4

The complete mathematical model for this problem is:

Maximize: 360x1 + 240x2 + 360x3 + 480x4

Subject to:

x1 = 50

x2 + x3 = 100

x16 + x28 + x34 + x410 <= 480

x14 + x26 + x32 + x48 <= 400

x14 + x24 + x34 + x46 <= 400

x1 >= 0

x2 >= 0

x3 >= 0

x4 <= 25

This model can be solved using linear programming techniques to find the values of x1, x2, x3, and x4 that maximize the total profit while satisfying all of the constraints. In this case, the optimal solution is x1 = 50, x2 = 100, x3 = 100, and x4 = 0, which corresponds to manufacturing 50 units of product I, 100 units of product II, and 100 units of product III each week. This meets all of the contractual obligations and maximizes the total profit.

Answer 2

The objective is to maximize total profit, which is given as

P = 360 [tex]x_1[/tex]+ 240[tex]x_2[/tex]+ 360[tex]x_3[/tex] + 480[tex]x_4[/tex]

What is Linear Programming Problem?

The goal of the Linear Programming Problems (LPP) is to determine the best value for a given linear function. The ideal value may be either the highest or lowest value. The specified linear function is regarded as an objective function in this situation.

Let[tex]x_1[/tex] , [tex]x_2[/tex],  [tex]x_3[/tex] and  [tex]x_4[/tex] be the number of units of product I, II, III and IV to be produced, respectively.

The constraints are that the time requirements for each product should not exceed the available time, the firm is contractually obligated to produce 50 units of product I and 100 units of products II and III, and the firm can sell at most 25 units of product IV.

These constraints can be written mathematically as:

3[tex]x_1[/tex]  + 2 [tex]x_2[/tex]+ 2 [tex]x_3[/tex]   + 4[tex]x_4[/tex] ≤ 480  (Machining)

[tex]x_1[/tex] +  [tex]x_2[/tex] +  [tex]x_3[/tex]   + 3[tex]x_4[/tex] ≤ 400  (Polishing)

2[tex]x_1[/tex]  +  [tex]x_2[/tex]+ 2 [tex]x_3[/tex]  + [tex]x_4[/tex] ≤ 400 (Assembling)

and, [tex]x_1[/tex]  ≥ 50 (Product I)

[tex]x_2[/tex] +  [tex]x_3[/tex]  ≥ 100 (Products II and III)

[tex]x_4[/tex] ≤ 25 (Product IV)

[tex]x_1[/tex] , [tex]x_2[/tex],  [tex]x_3[/tex]  , [tex]x_4[/tex] ≥ 0

Learn more about Linear Programming Problem here:

https://brainly.com/question/29405467

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Related Questions


The graph of f (x) = (x - 2)² + 1 is shown below. What would the new equation of the function be if it is shifted up 2 units?

Answers

Answer:

f (x) = (x - 2)² + 3

Step-by-step explanation:

Adding 2 to the constant k would shift the entire equation upwards by 2.

Apr 08, 12:51:17 AM
Brittney wants to buy grapes and apples to bring to a party. Grapes cost $1.60
per pound and apples cost $1.75 per pound. If she only has $10 to spend on
grapes and apples, which inequality represents the situation where she buys x
pounds of grapes and y pounds of apples?
1.60x + 1.75y < 10
1.60x + 1.75y > 10
Submit Answer
1.75x + 1.60y < 10
1.75% + 1.60y > 10
Type here to search
O
12:5
4/8/

Answers

Answer: did you get a answer yet?

Step-by-step explanation:

In a survey at a shoe store, 200 customers were asked whether they have
running shoes or basketball shoes. The results are in the relative frequency
table.
Total
Have running shoes
0.23
Have basketball shoes
No basketball shoes
Total
No running shoes
0.31
0.32
0.14
What percentage of the people surveyed have basketball shoes?
A. 37%
B. 54%
O C. 46%
O D. 63%

Answers

Ok I think is there go check 1 more time I think is c or b not completely sure

WILL MARK BRAINLYEST


A street sign is 8 feet tall and casts a shadow that is 28 feet long. At the same time, a nearby tree casts a shadow that is 210 feet long. How tall is the tree?

A.60
B.70
C.80
D.90

Answers

The answer is 60



Explanation: The shadows are 3.5 times bigger than the original height so you divide 210 by 3.5 and you get 60. I hope this helped.

Round 12,628 to nearest 1,000

Answers

Answer:

13000

Step-by-step explanation:

it's closer to 13000 than to 12000

Answer:

13000

Step-by-step explanation:

12628 >>>13000

Me:

This is easy like what grade are you in?

A minute- hand of a clock is 16 in long. Find the distance traveled by the tip of the minute - hand in one hour.

Answers

Answer: 16/2=8
8 * 8 = 64
64* 3.14 = 200.96
200.96 * 60 = 12057.6

Hope this helps (:

Need the answer for x and y

Answers

Answer:

See below

Step-by-step explanation:

There is no 'y' in your question but I will answer the Q in the pic:

  the two sides are equal    so

10x-1 = 8x+11

2x = 12

x = 6                 then CD = 8x+11 = 8(6)+ 11 = 59  units

The quadratic equation y = –6x2 + 100x – 180 models the store’s daily profit, y, for selling soccer balls at x dollars.
The quadratic equation y = –4x2 + 80x – 150 models the store’s daily profit, y, for selling footballs at x dollars. Use a graphing calculator to find the intersection point(s) of the graphs, and explain what they mean in the context of the problem.

Answers

Answer:

The quadratic equation y = -4x2 + 80x - 150 models the store's daily profit, y, for selling footballs at x dollars. you can subtract 150 from both sides and use the quadratic formula to find x=4. It can make at most 120 units in one day. 3 1. Backward Bending Supply Curve.

HELP PLEASEEEE!!! SOMEONE HELP ME FOR ONCE, NO ONE IS ANSWERING MY QUESTIONS AND IM SO FREAKING STRESSED OUT. OH MY GOD SOMEONE PLS IM BEGGING YOU EXPLAIN YOUR ANSWER STEP BY STEP FOR ONCE

In 1985 an antique automobile club had 23,000 members. Since then its membership has grown at an average rate of 5% per year. Assuming this trend continues, how many members will there be in 2020? Round to the nearest thousand.
a) 112,000 members
b) 78,000 members
c) 151,000 members
d) 127,000 members

Answers

Answer:

I have come to the conclusion that it is A. 112,000

Answer:

d) 127,000 members

Step-by-step explanation:

In this problem we have an exponential function of the form

where  a is the initial value

b is the base

The base is equal to  b=1+r

r is the average rate

In this problem we have  a=23,000 members

r=5%=5/100=0.05

b=1+0.05=1.05

substitute

x ----> is the number of years since 1985

How many members will there be in 2020?

x=2020-1985=35 years

substitute in the function

Round to the nearest thousand

Find the dot product of vectors u = -4i + 7j and v = 2i + j

Answers

Answer:

The desired dot product is -1

Step-by-step explanation:

To find the dot product of the given vectors, multiply the magnitudes of the 'i' and 'j' terms together, separately, and then add the results:

dot product of u and v = (-4)(2) + (7)(1) = -8 + 7 = -1

The desired dot product is -1

Need the answer for x and y

Answers

Answer:

x = 7°

y = 10°

Step-by-step explanation:

7x = 49

x = 7°

180 = 13y + 1 + 49

combine like terms:

13y = 130

y = 10°

Answer:

X equals to 7 & y equals to 10 'cause ;

7X=49

X=7

50 + 13 y + 1 = 180

13y = 130

y=10

Step-by-step explanation:

Good luck.

hope it was helpful for u .

Find the surface area of the rectangular prism (above) using its net (below).

Correct answer will receive a cookie and branilist

Answers

Answer:

62

Step-by-step explanation:

15+15+10+10+6+6= 62

5. A company intends to collect a random sample of size n from a population
with population proportion of interest p. Which of the following situations would
result in the smallest standard deviation of the sampling distribution of p?

Answers

Answer:D

Step-by-step explanation:

The situations that would result in the smallest standard deviation of p is; The population proportion p ≠ 0.5, and the sample size is n.

What is the standard deviation?

The formula for the standard deviation here is;

SD = √(n(p(1 - p))

Now, for the standard deviation to be maximum, it means that p = 0.5 and as such 1 - p will also be 0.5.

However, for Standard deviation to be smallest, then it means that p ≠ 0.5.

Secondly, for the sample size, it will have to remain as n and not 2n because when we say 2n, we are increasing the sample size which will in turn increase the standard deviation.

Read more about standard deviation at;

help plese i beg of you

Answers

9514 1404 393

Answer:

k = 45 . . . miles per hourk = 1/45 . . . hours per mile

Step-by-step explanation:

One way we can relate distance and time is ...

  time = k × distance

Then the value of k (the constant of proportionality) is ...

  k = time/distance = 4 hours/(180 miles)

  k = (1/45) hours/mile

__

Another way we can relate the variables is ...

  distance = k × time

Then the value of k (the constant of proportionality) is ...

  k = distance/time = (180 miles)/(4 hours)

  k = 45 miles/hour

Plz help NO LINKS this is due today

Answers

Answer:

It is C, the metric system

Hakima and Joshua both opened savings accounts. Both started with a balance of zero dollars. For every $3 that Hakima saves in her account, Joshua saves $5. If they have saved a total of $336, how much did Hakima save?

Answers

I’m pretty sure that would be $112

PLEASE HELP!!!!!!!!!! BRAINLIEST
Add the following fractions. Simplify and reduce to the lowest terms.

9/16 + 3/16

Answers

Answer:

3/4

Step-by-step explanation:

12/16

divided by 4

3/4

Answer: /34

Step-by-step explanation:

 9/16 + 3/16

=(9+3)/16 ⇔ Fractions with the same denominator can subtract or add

=12/16 ⇔ Simplify

=(3×4)/(4×4) ⇔ Factor each number

=3/4 ⇔ Divide 4 on both numerator and denominator

Hope this helps!! :)

Please let me know if you have any questions

Find the slope of the line that passes through the given points.

Answers

Answer: -1/6

Step-by-step explanation:

slope= change of y over change of x

3-4/ 5--1=

-1/6

Hope this helps!

Answer:

-1/6

Step-by-step explanation:

(-1, 4) and (5, 3)

y2 - y1 / x2 - x1

y2 = 3

y1 = 4

x2 = 5

x1 = -1

(3 - 4) / (5 - -1)

-1 / 6

slope = -1/6

What is the y-intercept for this function?
y = x2 - 2x - 3

Answers

Answer:

-3

Step-by-step explanation:

5, 4, 16/5 find the 7th term

Answers

Answer:

a₇ = [tex] \frac{4096}{3125} [/tex]

ILL GIVE THE BRAINLIEST pls help me with this question EVERYTHING IS IN THE PICTURE PLS HELP DUE TODAY ​​IF YOU PUT A WRONG ANSWER ILL REPORT YOU FASTER THAN ASSIGMENT IS DUE ​​​

Answers

Answer:

It is 47.5 or 47 1/2

Step-by-step explanation:

The formula for volume of a prism is base x height.

The base is the area of the rectangle at the bottom. The area of a rectangle is, of course, length times width, so 2.5 x 4=10.

So, the base is 10.

Now, the second part of the formula is height.

The height is 4.75.

Now, do the formula: Base x height : 10 x4.75

The answer is 47.5.

Don't report me lol. I promise it is correct.

Answer:

I need 5 Brainliest before I can become Ace

Step-by-step explanation:

17. An equation is shown.
3x7=+7
What number makes the number sentence true?
A 3
B, 14
C. 21
D. 28

Answers

the answer is 1 because 1x7=+7

6(5 - 8n) + 12 = -54
please step my step

Answers

Answer:

Look Below

Step-by-step explanation:

6(5 - 8N) + 12 = -54

-48N + 30 + 12 = -54

-48N + 42 = -54

(-48N + 42) + (-42) = -54 + (-42)

-48N = -96

-48N / 48 = N

-96 / 48 = 2

N = 2

Hope This Helps! If you find any fault in my answer please let me know. Thanks! Have a good day!

90:(3+6)-20.(60-55) propiedad

Answers

Answer:

https://www.commoncoresheets.com/Math/Properties/Applying%20Properties%20of%20Operations/Spanish/2.pdf

Step-by-step explanation:

This will help you:) not a spam link its a pdf that brings you straight to the worksheet <3

Which algebraic expression represents the phrase "the quotient of negative eight and the sum of a number and three"
-8
Og+3
8
9+3
-8+g
3
+3

Answers

Answer:

[tex]\dfrac{-8}{x+3}[/tex]

Step-by-step explanation:

We need to find an algebraic expression for the given statement i.e. "the quotient of negative eight and the sum of a number and three".

Let the number be x. Quotient means to divide. It means we need to divide -8 and the sum of x and 3.

So, we can write it as follows :

[tex]\dfrac{-8}{x+3}[/tex]

Hence, this is the required solution.

Help asap
Find the value of x. Round to the
nearest tenth.
3
4
X =
= [?]

Answers

Answer:

36.9°

Step-by-step explanation:

→ Identify the triangle required by seeing which side is not given

Hypotenuse is not given so we need to use Tan⁻¹ = Opposite / Adjacent

→ Substitute values in

Tan⁻¹ =  ( 3 ÷ 4 )

→ Simplify

36.9°

for the following problems do at least one problem using unit form and at least one problem using fraction form 3.2 x 1.4=

Answers

the one above me was correct just did it^^

The area of a rectangular living room is 264 square feet. The length of the room is 2 feet less than twice the width.
What is the width of the living room in feet?

Answers

9514 1404 393

Answer:

  12 ft

Step-by-step explanation:

Let the width of the room be represented by w. Then the length is (2w-2), and the area is ...

  A = LW

  264 = (2w-2)w

  132 = w² -w . . . . . . . divide by 2, eliminate parentheses

  132.25 = w² -w +.25 . . . . . add (-1/2)² to complete the square

  √132.25 = w -0.5 . . . . . take the square root

  0.5 +11.5 = w = 12 . . . . . add 0.5; use the positive root

The width of the living room is 12 feet.

Solve x2 + 6x = 7 by completing the square. Which is the solution set of the equation?

Answers

Use the formula b over 2 squared In order to create a new term, solve for x by using this term to complete the square. X= 1, -7

-6x+8y=12 and -3x+4y=6

Answers

Answer:

3441

Step-by-step explanation:

PLS HOPE THIS HELP

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