Question

Find the minimum value of P=5x+6y subject to the following constraints.
Please help me!!

Answer 1

The maximum value of P is 34 and the minimum value of P is 0

Explanation:

we have the following constraints

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

`2x+3y \leq 16` ----> constraint B

`x\geq 0` ----> constraint C

`y\geq 0` ----> constraint D

Solve the feasible region by graphing

Using a graphing tool

The vertices of the feasible region are

(0,0),(0,5.33),(2,4),(6,0)

see the attached figure

To find out the maximum and minimum value of the objective function P, substitute the value of x and the value of y for each of the vertices in the objective function P, and then compare the results

we have

`P=5x+6y`

For (0,0) ---->
`P=5(0)+6(0)=0`

For (0,5.33) ---->
`P=5(0)+6(5.33)=31.98`

For (2,4) ---->
`P=5(2)+6(4)=34`

For (6,0) ---->
`P=5(6)+6(0)=30`

therefore

The maximum value of P is 34 and the minimum value of P is 0