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A Sporting Goods Company makes basketballs and footballs. Each product is produced from two resources-rubber and leather. The resource requirements for each product and the total resources available are as follows: Resource requirements per Unit Product Rubber (Ib) Leather ft? Basketball 3 4 Football 2 Total resources 500lb 800ft? available Each basketball produced results in a profit of $12 and each football earns $16 in profit. a) Formulate a linear programming model to determine the number of basketballs and footballs to produce in order to maximize profit. b) Transform this model into standard form. c) Solve the model formulated by using graphical analysis d) Are there any binding constraint(s)? If Yes/No Explain Question 2 Using the information in question 1 of the Sporting Goods Company, answer the following: a) Identify the number of unused resources (i.e., slack) at each of the graphical extreme points (8) b) What would be the effect on the optimal solution if the profit for a basketball changed from $12 to $13? c) What would be the effect if the profit for a football changed from $16 to $15? d) What would be the effect on the optimal solution if 500 additional pounds of rubber could be obtained? What would be the effect if 500 additional square feet of leather could be obtained?

A Sporting Goods Company makes basketballs and footballs. Each product is produced from two resources-rubber and leather. The resource requirements for each product and the total resources available are as follows: Resource requirements per Unit Product Rubber (Ib) Leather ft? Basketball 3 4 Football 2 Total resources 500lb 800ft? available Each basketball produced results in a profit of $12 and each football earns $16 in profit. a) Formulate a linear programming model to determine the number of basketballs and footballs to produce in order to maximize profit. b) Transform this model into standard form. c) Solve the model formulated by using graphical analysis d) Are there any binding constraint(s)? If Yes/No Explain Question 2 Using the information in question 1 of the Sporting Goods Company, answer the following: a) Identify the number of unused resources (i.e., slack) at each of the graphical extreme points (8) b) What would be the effect on the optimal solution if the profit for a basketball changed from $12 to $13? c) What would be the effect if the profit for a football changed from $16 to $15? d) What would be the effect on the optimal solution if 500 additional pounds of rubber could be obtained? What would be the effect if 500 additional square feet of leather could be obtained?

Practical Management Science
Practical Management Science
6th Edition
ISBN:9781337406659
Author:WINSTON, Wayne L.
Publisher:WINSTON, Wayne L.
Chapter5: Network Models
Section5.3: Assignment Models
Problem 12P
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pleqse solve the question 2 here using the information in question 1

A Sporting Goods Company makes basketballs and footballs. Each product is produced from two resources-rubber and leather. The resource requirements for each product and the total resources available are as follows: Resource requirements per Unit Product Rubber (Ib) Leather ft? Basketball 3 4 Football 2 Total resources 500lb 800ft? available Each basketball produced results in a profit of $12 and each football earns $16 in profit. a) Formulate a linear programming model to determine the number of basketballs and footballs to produce in order to maximize profit. b) Transform this model into standard form. c) Solve the model formulated by using graphical analysis d) Are there any binding constraint(s)? If Yes/No Explain
Transcribed Image Text:A Sporting Goods Company makes basketballs and footballs. Each product is produced from two resources-rubber and leather. The resource requirements for each product and the total resources available are as follows: Resource requirements per Unit Product Rubber (Ib) Leather ft? Basketball 3 4 Football 2 Total resources 500lb 800ft? available Each basketball produced results in a profit of $12 and each football earns $16 in profit. a) Formulate a linear programming model to determine the number of basketballs and footballs to produce in order to maximize profit. b) Transform this model into standard form. c) Solve the model formulated by using graphical analysis d) Are there any binding constraint(s)? If Yes/No Explain
Question 2 Using the information in question 1 of the Sporting Goods Company, answer the following: a) Identify the number of unused resources (i.e., slack) at each of the graphical extreme points (8) b) What would be the effect on the optimal solution if the profit for a basketball changed from $12 to $13? c) What would be the effect if the profit for a football changed from $16 to $15? d) What would be the effect on the optimal solution if 500 additional pounds of rubber could be obtained? What would be the effect if 500 additional square feet of leather could be obtained?
Transcribed Image Text:Question 2 Using the information in question 1 of the Sporting Goods Company, answer the following: a) Identify the number of unused resources (i.e., slack) at each of the graphical extreme points (8) b) What would be the effect on the optimal solution if the profit for a basketball changed from $12 to $13? c) What would be the effect if the profit for a football changed from $16 to $15? d) What would be the effect on the optimal solution if 500 additional pounds of rubber could be obtained? What would be the effect if 500 additional square feet of leather could be obtained?
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