Chapter 3.6, Problem 5P

Explanation of Solution

 Maximization of Net Present Value (NPV) of Finco:

 In the given information, each dollar invested reduces the NPV of the company by $10\cancel{\text{c}}$ and each of debt increases the NPV by 50$10\cancel{\text{c}}$.

 Let the investment done by Fincobe x₁ and debt taken by him be x₂.

 The NPV of the company is,

 $\text{NPV = -10}{x}_1+50x_2$

 This NPV is to be maximized. So the objective function for the Linear Programming (LP) is.

 $\text{Max z = -10}{x}_1+50x_2$

 The provided constraints are:

 Constraint 1:

 Finco can invest at most $1 million during the coming year that is the investment should be less than $1 million, so the constraint formed is:

 $x_1\le 1000000$

 Constraint 2:

 At most 40% of investment in the debt. So, the constraint formed is:

 $x_2\le 0.4x_1$

 Constraint 3:

 Finco now has $800000 in cash available. All the investment must be paid for from the current cash or borrowed money. So, all the investments and debts must be paid from current cash of $800000