A company manufactures both mountain bikes and trail bikes. The cost of materials for a mountain bike is $60, and the cost of materials for a trail bike is $40. The cost of labor to manufacture a mountain bike is $80, and the cost of labor to manufacture a trail bike is $60. During a week in which the company has budgeted $1,800 for materials and $2,500 for labor, how many mountain bikes does the company plan to manufacture? mountain bikes

A company manufactures both mountain bikes and trail bikes. The cost of materials for a mountain bike is $60, and the cost of materials for a trail bike is $40. The cost of labor to manufacture a mountain bike is $80, and the cost of labor to manufacture a trail bike is $60. During a week in which the company has budgeted $1,800 for materials and $2,500 for labor, how many mountain bikes does the company plan to manufacture? mountain bikes

Practical Management Science

6th Edition

ISBN:9781337406659

Author:WINSTON, Wayne L.

Publisher:WINSTON, Wayne L.

Chapter6: Optimization Models With Integer Variables

Section6.6: Cutting Stock Models

Problem 37P

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The Pigskin Company produces footballs. Pigskin must decide how many footballs to produce each month. The company has decided to use a six-month planning horizon. The forecasted monthly demands for the next six months are 10,000, 15,000, 30,000, 35,000, 25,000, and 10,000. Pigskin wants to meet these demands on time, knowing that it currently has 5000 footballs in inventory and that it can use a given months production to help meet the demand for that month. (For simplicity, we assume that production occurs during the month, and demand occurs at the end of the month.) During each month there is enough production capacity to produce up to 30,000 footballs, and there is enough storage capacity to store up to 10,000 footballs at the end of the month, after demand has occurred. The forecasted production costs per football for the next six months are 12.50, 12.55, 12.70, 12.80, 12.85, and 12.95, respectively. The holding cost incurred per football held in inventory at the end of any month is 5% of the production cost for that month. (This cost includes the cost of storage and also the cost of money tied up in inventory.) The selling price for footballs is not considered relevant to the production decision because Pigskin will satisfy all customer demand exactly when it occursat whatever the selling price is. Therefore. Pigskin wants to determine the production schedule that minimizes the total production and holding costs. Can you guess the results of a sensitivity analysis on the initial inventory in the Pigskin model? See if your guess is correct by using SolverTable and allowing the initial inventory to vary from 0 to 10,000 in increments of 1000. Keep track of the values in the decision variable cells and the objective cell.
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