Chapter 4.1, Problem 29E

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.

Production—Jackets A charity wants to produce as many jackets as possible before winter starts for people living in a refugee camp. They have 3 styles of jackets they can produce. The first requires 6 sq ft of nylon fabric and 2 sq ft of fleece. The second requires 4 sq ft of nylon and 3 sq ft of fleece, while the third requires 3 sq ft of nylon and 5 sq ft of fleece. The costs to produce each of the three styles of jackets are $20, $18, and $17, respectively. If they have $600 available to spend on this project, and if 300 sq ft of nylon and 150 sq ft of fleece are available, what is the maximum number of jackets they can produce, and how many of each style should be produced?