MBA 780Fall 2006 Linear Programming (TN 2)
Illustration (Anderson, Sweeney & Williams, 11/e)
Kelson Sporting Equipment, Inc. makes two different types of baseball gloves: a regular model and a catcher’s mitt. The firm has 900 hours of production time available in its cutting & sewing department, 300 hours available in its finishing department, and 100 hours available in its packaging & shipping department. The production time requirements and the unit profit contributions are as follows:
Production Time (hours)Model / Cutting & Sewing / Finishing / Packaging & Shipping / Profit/glove
Regular / 1 / 1/2 / 1/8 / $5
Catcher’s / 3/2 / 1/3 / 1/4 / $8
Assume that the firm wishes to maximize the total profit. Formulate the appropriate linear programming (LP) model and find an optimal solution, (a) using the graphical approach, (b) and a spreadsheet application. Interpret the optimal solution found.
Assignment 1, due September 20, 2006.
The production manager for the Classic Boat Corporation must determine how many units of the Classic 21 model to produce over the next four quarters. The company has a beginning inventory of 100 Classic 21 boats, and demand for the four quarters is 2000 units in quarter 1, 4000 units in quarter 2, 3000 units in quarter 3, and 1500 units in quarter 4. The firm has limited capacity in each quarter. That is, up to 4000 units can be produced in quarter 1, 3000 units in quarter 2, 2000 units in quarter 3, and 4000 units in quarter 4. Each boat held in inventory in quarters 1 and 2 incurs an inventory holding cost of $250/unit; the holding cost for quarters 3 and 4 is $300 per unit. The production costs for the first quarter amount to $10,000 per unit; these costs are expected to increase by 10% each quarter because of increases in labor & material costs. Management has specified that the ending inventory for quarter 4 must be at least 500 boats. (Anderson, Sweeney & Williams, 11/e.)
(a) Formulate a linear programming model that can be used to determine the production schedule that will minimize the total cost of meeting demand in each quarter, subject to the production capacities in each quarter and also to the required ending inventory in quarter 4.
(b) Use the Excel Solver to solve the LP model from part (a) and explain the optimal solution verbally.
(c) Interpret the dual prices corresponding to the constraints developed to meet demand in each quarter. What do these dual prices tell the production manager?
(c) Interpret the dual prices corresponding to the production capacity constraints in each quarter. What do these dual prices tell the production manager?
(Please cut and paste so that your answer to each part begins on a new page.)