Question: You would have to make a linear program with constraints. I just don't know how Exercise 5.7 A paper company manufactures three basic products: pads



You would have to make a linear program with constraints. I just don't know how
Exercise 5.7 A paper company manufactures three basic products: pads of paper, 5-packs of paper, and 20-packs of paper. The pad of paper consists of a single pad of 25 sheets of lined paper. The 5-pack consists of 5 pads of paper, together with a small notebook. The 20-pack of paper consists of 20 pads of paper, together with a large notebook. The small and large notebooks are not sold separately. Production of each pad of paper requires 1 minute of paper-machine time, 1 minute of supervisory time, and $.10 in direct costs. Production of each small notebook takes 2 minutes of paper-machine time, 45 seconds of supervisory time, and $.20 in direct cost. Production of each large notebook takes 3 minutes of paper machine time, 30 seconds of supervisory time and $.30 in direct costs. To package the 5-pack takes 1 minute of packager's time and 1 minute of supervisory time. To package the 20-pack takes 3 minutes of packager's time and 2 minutes of supervisory time. The amounts of available paper-machine time, supervisory time, and packager's time are constants b, 62, 63, respectively. Any of the three products can be sold to retailers in any quantity at the prices $.30, $1.60, and $7.00, respectively. Provide a linear programming formulation of the problem of determining an optimal mix of the three products. (You may ignore the constraint that only integer quantities can be produced.) Try to formulate the problem in such a Sec. 5.7 Exercises 225 way that the following questions can be answered by looking at a single dual variable or reduced cost in the final tableau. Also, for each question, give a brief explanation of why it can be answered by looking at just one dual price or reduced cost. (a) What is the marginal value of an extra unit of supervisory time? (b) What is the lowest price at which it is worthwhile to produce single pads of paper for saleStep by Step Solution
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