chwinn holds 3 type of bicycles: race bikes, cross-country bikes, and trail bikes. He sells race bikes for $1,900, cross-country bikes for $2,200 and trail bikes for $1300. A race bike costs $1,300, a cross-country bike costs $1,800 and a trail bike costs $1000. He has $12,000 available this month to purchase bikes. Each bike requires assembly: a race bike requires 8 hours to assemble, a cross-country bike requires 12 hours, and a trail bike requires 16 hours. He and his employees have 120 hours available to put the bikes together. He has enough space in his store to order 20 bikes this month. Schwinn wants to stock at least twice as many trail bikes as the other two combined. A. Formulate a linear programming model for this problem. B. Solve the linear programming model using excel Solver. What is the maximum profit? C. How many bicycles should he purchase from each?
chwinn holds 3 type of bicycles: race bikes, cross-country bikes, and trail bikes. He sells race bikes for $1,900, cross-country bikes for $2,200 and trail bikes for $1300. A race bike costs $1,300, a cross-country bike costs $1,800 and a trail bike costs $1000. He has $12,000 available this month to purchase bikes. Each bike requires assembly: a race bike requires 8 hours to assemble, a cross-country bike requires 12 hours, and a trail bike requires 16 hours. He and his employees have 120 hours available to put the bikes together. He has enough space in his store to order 20 bikes this month. Schwinn wants to stock at least twice as many trail bikes as the other two combined. A. Formulate a linear programming model for this problem. B. Solve the linear programming model using excel Solver. What is the maximum profit? C. How many bicycles should he purchase from each?
Practical Management Science
6th Edition
ISBN:9781337406659
Author:WINSTON, Wayne L.
Publisher:WINSTON, Wayne L.
Chapter4: Linear Programming Models
Section4.4: Aggregate Planning Models
Problem 15P
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- Schwinn holds 3 type of bicycles: race bikes, cross-country bikes, and trail bikes. He sells race bikes for $1,900, cross-country bikes for $2,200 and trail bikes for $1300. A race bike costs $1,300, a cross-country bike costs $1,800 and a trail bike costs $1000. He has $12,000 available this month to purchase bikes. Each bike requires assembly: a race bike requires 8 hours to assemble, a cross-country bike requires 12 hours, and a trail bike requires 16 hours. He and his employees have 120 hours available to put the bikes together. He has enough space in his store to order 20 bikes this month. Schwinn wants to stock at least twice as many trail bikes as the other two combined.
A. Formulate a linear programming model for this problem.
B. Solve the linear programming model using excel Solver. What is the maximum profit?
C. How many bicycles should he purchase from each?
D. What should Schwinn do to increase profit based on the optimal solution?
E. If Schwinn hired an additional worker for 40 hours at least $10 per hour, how much additional profit would he make, if any?
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