Question

Maximize Y=1.44-0.05x-0.04y, using the constraints: x>=0, y>=0, y>=-x+10, y<=-x+15, and y<=(2)/(3)x. What is the maximum value of Y under these constraints?

A) 0.75
B) 0.69
C) 0.98
D) 0.94

Answer 1

To maximize Y = 1.44 - 0.05x - 0.04y with given constraints, graph the feasible region and evaluate the objective function Y at each corner point to find the maximum value.

Step-by-step explanation:

To maximize the value of Y = 1.44 - 0.05x - 0.04y, we need to find the corner points of the feasible region defined by the given constraints: x ≥ 0, y ≥ 0, y ≥ -x + 10, y ≤ -x + 15, and y ≤ (2/3)x.

By graphing the constraints, we find that the feasible region is a pentagon with vertices at (0,10), (0,15), (9,1), (10,0), and (15,0). We can evaluate the objective function Y at each of these corner points to determine the maximum value.

After substituting the x and y values from each corner point into the objective function Y, we find that the maximum value of Y is 0.75 when x = 9 and y = 1.