Question

Formulate but do not solve the following exercise as a linear programming problem. A financier plans to invest up to $400,000 in two projects. Project A yields a return of 9% on the investment of x dollars, whereas Project B yields a return of 16% on the investment of y dollars. Because the investment in Project B is riskier than the investment in Project A, the financier has decided that the investment in Project B should not exceed 40% of the total investment. How much should she invest in each project in order to maximize the return on her investment, P?

A) Maximize P=0.09x+0.16y

B) Subject to x+y≤400,000 and y≤0.4x

C) x≥0 and y≥0

D) All of the above

Answer 1

Formulate the given exercise as a linear programming problem by defining decision variables, objective function, and constraints. The correct formulation is subject to x+y≤400,000 and y≤0.4x.

Step-by-step explanation:
To formulate the given exercise as a linear programming problem, we need to define the decision variables, objective function, and constraints.

Let x represent the amount invested in Project A (in dollars)
Let y represent the amount invested in Project B (in dollars)
Objective Function:
We want to maximize the return on the investment, which is represented by P. So, the objective function is P = 0.09x + 0.16y.
Constraints:
1. The total investment should not exceed $400,000: x + y ≤ 400,000.
2. The investment in Project B should not exceed 40% of the total investment: y ≤ 0.4x.

Therefore, the linear programming problem can be formulated as follows:
Maximize P = 0.09x + 0.16y
Subject to: x + y ≤ 400,000 and y ≤ 0.4x