Chapter 4.3, Problem 54E

In Problems 49-54, use Excel to solve each linear programming problem.

Investment analysis Conglomo Corporation is considering investing in other smaller companies, and it can purchase any fraction of each company. Each investment by Conglomo requires a partial payment now and a final payment 1 year from now. For each investment, the following table summarizes the amount of each payment (in millions of dollars) and the projected 5-year profit (also in millions of dollars).

	Company Company Company Company Company
	1	2	3	4	5
Paid now Paid in	13.2	63.6	6.0	6.0	34.8
1 year Projected	3.6	7.2	6.0	1.2	40.8
profit	15.6	19.2	19.2	16.8	46.8

This table may be interpreted as follows: If Conglomo purchases one-fifth of Company 4, then it pays $\frac{1}{5}\left(6.0\right)=\$1.2$ million now and $\frac{1}{2}\left(1.2\right)=\$0.24$ million = $240,000 after 1 year, and the one-fifth share has a projected 5-year profit of $\frac{1}{5}(16.8)=\$3.36$ million. Conglomo has $48 million available for investment now and $24 million available for investment 1 year from now. What fraction of each smaller company should Conglomo purchase to maximize the projected 5-year profit? What is the maximum profit? Hint: If $x_1$ represents the fraction of Company 1 that is purchased, then $x_{\text{1}}\le 1$ is a constraint.