Formulate but do not solve the problem.

The management of a private investment club has a fund of$300,000earmarked for investment in stocks. To arrive at an acceptable overall level of risk, the stocks that management is considering have been classified into three categories: high-risk, medium-risk, and low-risk. Management estimates that high-risk stocks will have a rate of return of14%/year; medium-risk stocks,11%/year; and low-risk stocks,6%/year. The investment in low-risk stocks is to be twice the sum of the investments in stocks of the other two categories. If the investment goal is to have an average rate of return of 9%/year on the total investment, determine how much the club should invest in each type of stock. (Assume that all the money available for investment is invested. Letx,y, andzdenote the amount, in dollars, invested in high-, medium-, and low-risk stocks, respectively.)

=300,000

=z

= .09(300,000)

Formulate but do not solve the problem.

The management of Hartman Rent-A-Car has allocated$2.24million to buy a fleet of new automobiles consisting of compact, intermediate-size, and full-size cars. Compacts cost$16,000each, intermediate-size cars cost$24,000each, and full-size cars cost$32,000each. If Hartman purchases twice as many compacts as intermediate-size cars and the total number of cars to be purchased is 100, determine how many cars of each type will be purchased. (Assume that the entire budget will be used. Letx,y, andzdenote the number of compact, intermediate-sized, and full-size cars purchased, respectively.)

=2,240,000

=x

= 100