Question

Please help! For the feasibility region shown below, find the maximum value of the function: P= -3x+4y.

Answer 1

please help, i dont understand what im supposed to do at all :(

Answer 2

i think it is 0,8

Answer 3

how did you get that? @ask1709

Answer 4

The point that gives the maximum value of the function must lie within the feasibility region which is cross-hatched in the diagram.
P = -3x + 4y is a family of straight lines.
The function can be rearranged into the form y = mx + b giving:
y = 3/4 x + P/4 where the slope is 3/4 and the y-intercept is P/4.
On the diagram the maximum value of P/4 is at the point (0, 8). Plugging these values of x and y into the original function gives the maximum value:
P = -3 * 0 + 4 * 8 = 32

Answer 5

thank you @kropot72!

Answer 6

@kropot72 can you please help me with this problem? i tried doing what you explained above but the negatives are throwing me off :(

Answer 7

In this second case the function can be rearranged to:
y = -3/2 x + P/2 and the maximum value of the y-intercept P/2 is when the line touches the point (6, 5).
Plugging these values of x and y into the original function gives the maximum value:
P = 3 * 6 +2 * 5 = 28

Answer 8

thank you so much @kropot72 !!! i would give extra medals if i could!

Answer 9

You're welcome :)