Chapter 4.1, Problem 27E

Set up Exercises 27–31 for solution by the simplex method. First express the linear constraints and objective function, then add slack variables to convert each constraint into a linear equation, and then set up the initial simplex tableau. The solutions of some of these problems will be completed in the exercises for the next section.

Business and Economics

27. Royalties The authors of a best-selling textbook in finite mathematics are told that, for the next edition of their book, each simple figure would cost the project $20, each figure with additions would cost $35, and each computer-drawn sketch would cost $60. They are limited to 400 figures, for which they are allowed to spend up to $2200. The number of computer-drawn sketches must be no more than the number of the other two types combined, and there must be at least twice as many simple figures as there are figures with additions. If each simple figure increases the royalties by $95, each figure with additions increases royalties by $200, and each computer-drawn figure increases royalties by $325, how many of each type of figure should be included to maximize royalties, assuming that all art costs are borne by the publisher?