Ascent, Inc. manufactures hiking boots. Demand for boots is highly seasonal. In particular, the demand in the next year is expected to be 3,000, 4,000, 8,000, and 7,000 pairs of boots in quarters 1, 2, 3, and 4, respectively. With its current production facility, the company can produce at most 6,000 pairs of boots in any quarter. Ascent would like to meet all the expected demand, so it will need to carry inventory to meet demand in the later quarters. Each pair of boots sold generates a profit of ₱1,000 per pair. Each pair of boots in inventory at the end of a quarter incurs ₱400 in storage and capital recovery costs. Ascent has 1,000 pairs of boots in inventory at the start of quarter 1. Ascent's top management has given you the assignment of modeling and analyzing what the production schedule should be for the next four quarters. In particular, you are asked to determine how many pairs of boots to produce in each quarter so that you satisfy the demand in each quarter. While doing so, you want to maximize the total annual profit, which is equal to the profit gained from sales minus the inventory costs. a. Formulate the above problem mathematically as a linear programming model. Define your decision variables clearly; define the notation you use, Using your decision variables, formulate the objective function and constraints. b. Suppose that Ascent were to produce 5,000 pairs of boots in each of the first two quarters. Calculate by hand what the ending positions would be for quarters 1 and 2. Expand the model to full scale and then solve it using Excel Solver. c. What is the recommended production schedule? What is the maximum profit that Ascent can get?
Ascent, Inc. manufactures hiking boots. Demand for boots is highly seasonal. In particular, the demand in the next year is expected to be 3,000, 4,000, 8,000, and 7,000 pairs of boots in quarters 1, 2, 3, and 4, respectively. With its current production facility, the company can produce at most 6,000 pairs of boots in any quarter. Ascent would like to meet all the expected demand, so it will need to carry inventory to meet demand in the later quarters. Each pair of boots sold generates a profit of ₱1,000 per pair. Each pair of boots in inventory at the end of a quarter incurs ₱400 in storage and capital recovery costs. Ascent has 1,000 pairs of boots in inventory at the start of quarter 1.
Ascent's top management has given you the assignment of modeling and analyzing what the production
a. Formulate the above problem mathematically as a linear programming model. Define your decision variables clearly; define the notation you use, Using your decision variables, formulate the objective function and constraints.
b. Suppose that Ascent were to produce 5,000 pairs of boots in each of the first two quarters. Calculate by hand what the ending positions would be for quarters 1 and 2.
Expand the model to full scale and then solve it using Excel Solver.
c. What is the recommended production schedule? What is the maximum profit that Ascent can get?
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