Question

Use the method of this section to solve the linear programming problem. Minimize c= (x^2) y subject to 4x−7y≤60, 2x+y=26, x≥0, y≥0. The minimum is:

a) c=169, at (x,y)=(13,0)
b) c=196, at (x,y)=(0,26)
c) c=144, at (x,y)=(0,20)
d) c=121, at (x,y)=(10,6)

Answer 1

To solve the linear programming problem, graph the feasible region and evaluate the objective function at each corner point to find the minimum value of c, which is 196 at (x, y) = (0, 26).

Step-by-step explanation:

To solve the linear programming problem, we can use the method of this section. The objective function is to minimize c = (x^2)y. We are given the following constraints: 4x - 7y ≤ 60, 2x + y = 26, x ≥ 0, and y ≥ 0.

First, we need to graph the feasible region, which is the intersection of the feasible set defined by the constraints. Then, we evaluate the objective function at each corner point (the vertices of the feasible region) to find the minimum value of c.

After evaluating the objective function at each corner point, we find that the minimum value of c is 196 at (x, y) = (0, 26). Therefore, the correct answer is b) c=196, at (x,y)=(0,26).