Maximize z=200x+300y subject to x+2y<10 ,x+y<6,x>4 and x>0 ,y>0
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Answer:

In theory I would have started looking at the critical points of the function, ie where the tangent plane is horizontal. Trick is, since the function is linear in both x and y the tangent plane is the curve itself, and it's never horizontal. We have to parametrize the border and look in there.

From the last two conditions ([tex]x>0; y>0[/tex]) we are looking only at the first quadrant. Let's start drawing lines.

The various restrains are color coded in the graph ([tex]x+2y<10[/tex] is red, [tex]x+y<6[/tex] is blue, [tex]x>4[/tex] is orange). That leads to the right triangle with a grey border that gets parametrized as shown. Due to the linearity of the original function, the maximum is at one of the extremes (upper or lower depending if the coefficient of the parameter is positive or negative). At this point is just calculating the values, pick up the largest, and see which points correspond to that value of the parameter.

Number crunching done, the maximum is at (4,2)

A moving company charges $450 plus $12 per hour. Another moving company charges $21 per hour. How long is the job that costs the same no matter which moving company is used?

The length of a rectangle is 6 in less than 3 times the width. If the perimeter is 36 in, what is the width of the rectangle?

Solve the problem using a system of equations: The difference of the squares of two numbers is 15. The difference of twice the square of the first number and the square of the second number is 30. Find the numbers.
(__,__),(__,__)

Question 5 of 10
Which of the following lists of ordered pairs is a function?
A. (1,6), (2, 7), (4,9), (0,5)
B. (2,4), (0, 2), (2, -4), (5,3)
C. (0,2), (2, 3), (0, -2), (4,1)
O D. (1,2), (1, -2), (3, 2), (3, 4)

Each day of Spirit Week at Alek's school, students have the option of dressing up according to a different theme. On Tuesday of Spirit Week, Alek recorded the number of students at his school by class and style of dress. Here is his data:

Find the value of x. Show all work.
(7x + 6)°
(6x - 7)º

April took out a $600 loan from the
bank. At the end of 5 years, she pays
back the principal, plus $60 simple
interest. What was the interest rate?

87 is 12.5% of what number?

The women's rights movement gained momentum in the 1960s as leaders like Betty Friedan and Gloria Steinem began sharing
their beliefs and concerns regarding discrimination against women. The Equal Rights Amendment called for an end to
discrimination based on gender. Which statement is true regarding the ERA?

The table shows a linear relationship between x and y.
x
-6
-3
1
4
Y
21
13.5
3.5
-4

What is the slope of the line represented by the values in the table?

Find the value of x.

Assuming that the data for all employees follows the same pattern, which kind of relationship is
there between years of higher education and current salary?
A- a clustered relationship
B- there is no relationship
C- a negative correlation
D- a positive correlation

Whats (c) ????????????? ????

100 POINT QUESTION!!!!!!!!!!!!!!!!!!!!!!!!!!!!

Solve 2x2 – 6x + 10 = 0 by completing the square.
Question 10 options:

A)

x = 3∕2 + 1∕2 i, x = 3∕2 – 1∕2i

B)

x = 3 + i, x = 3 – i

C)

x = 3∕2 + i , x = 3∕2 – i

D)

x = 3 + i, x = 3 – i

Perimeter of a trapezoid is 39a-7. Three sides have the following length 9a, 5a+1, and 17a-6 what is the length of the fourth side

There are 18x10/1 players in league

part A: The league raised $1,560 through fundraisers. Trenton estimates the cost of buying jackets for each players in the league. He concludes that the league has raised enough money. Do you agree with Trenton? Explain.



part B: how much would it cost to order sweatpants for each player? write and solve an equation with a variable to show your work.


1: Which cost more: 136 sweatpants or 103 sweatshirts? How much more?



Parts A: Coach sandberg wants to order 115 jackets and 27 caps for $12 each.

Estimate the total cost for his order. Show your work


what is his total cost? compare your answer to your estimate

Does anyone know this?

help pls anyone? pls​

what is a teachers most favorite tree

Start with x and cube it​

What is the sum in 1 1/3+ 2 1/3 + 3 2/3 + 4 1/2 + 5 1/2 + 6 3/4

What is 2+2=?
PLS HEP ME
I in kindergarden.

Would anyone be able to help with this?

Does anyone know the answer to this? Please help

What is an equation of the line that passes through the point (4, −1) and has
slope −5?

........................................

The students in art clas are designing a stained glass window to hang in the school entryway. The window wil
be 3 feet tall and 4 feet wide.
They have raised $100 for the project. The colored glass costs $5 per square foot and the dear glass costs $2
per square foot. The material they need to join the pieces of glass together costs to cents per foot and the
frame around the window costs $4 per foot
Do they have enough money to cover the cost of making the window.

Pahelp yawa T^T[tex]{\blue{\rule{25pt}{1pt}{\purple{\rule{30pt}{3pt}{\red{\rule{50pt}{5pt}{\purple{\rule{30pt}{3pt}{\blue{\rule{25pt}{1pt} }}}}}}}}}}︎︎︎︎︎︎︎︎ ︎︎︎︎︎︎︎︎[/tex]

pasagut 6-7 lang T^T
sabog na akow HAHAH​

use the correct trig function to find the value of x. (SAH,CAH,TAH)​

Can 4x + 10 can be simplified to 14x?