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Your friend is trying to find the maximum value of P = -x + 3y subject to the following four constraints.

• What error did your friend make in the graph below?

• What is the correct solution?

Your friend is trying to find the maximum value of P = -x + 3y subject to the following-example-1
User Laronda
by
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1 Answer

4 votes

Answer:

The maximum value of P=11 occurs at x=1 and y=4

Explanation:

we have


y\leq -2x+6 ----> constraint A


y\leq x+3 ----> constraint B


x\geq 0 ----> constraint C


y\geq 0 ----> constraint D

using a graphing tool

The solution is the shaded area

see the attached figure

The vertices of the solution area are

(0,0),(0,3),(1,4),(3,0)

Substitute the value of x and the value of y of each vertex in the objective function , to find out the maximum value of P

The objective function is


P=-x+3y

For (0,0) ----->
P=-(0)+3(0)=0

For (0,3) ----->
P=-(0)+3(3)=9

For (1,4) ----->
P=-(1)+3(4)=11

For (3,0) ----->
P=-(3)+3(0)=-3

therefore

The maximum value of P=11 occurs at x=1 and y=4

Your friend is trying to find the maximum value of P = -x + 3y subject to the following-example-1
User Tonka
by
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