Please find the attached file.DSS610 Quiz 4 Linear programming (NOTE: There is an Excel...

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Please find the attached file.DSS610		Quiz 4 Linear programming (NOTE:    There is an Excel Spreadsheet available for these problems but for the ones asking for “Standard Form” hardcopy/manual layout and computation will be expected besides using the spreadsheet and Solver. But Solver is available for you to use to check your manual answers.) 1. Southern Sporting Good Company makes basketballs and footballs which have profits of $12 and $16 respectively. 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 (lb.) 	Leather (ft2.) 	Basketball  	3 	4 	Football 	2 	5 	Total resources available 	500 lb. 	800 ft2 a. State the optimal solution (standard form) b. What would be the effect on the optimal solution if the profit for a basketball changes from $12 to $13? What would be the effect if the profit for a football changed from $16 to $15? c. 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? 2. A company produces two products, A and B, which have profits of $9 and $7, respectively. Each unit of product must be processed on two assembly lines where the required production times are as follows: 	 	Hours/Unit 	Product 	Line 1 	Line 2 	A 	12 	4 	B 	4 	8 	Total Hours 	60 	40 a. Formulate a linear programming model to determine the optimal product mix that will maximize profit. b. Transform this model into standard form. 3. Solve problem 2 using the computer (Solver) a. State the optimal solution b. What would be the effect on the optimal solution if the production time on line 1 was reduced to 40 hours? 4. For the linear programming model formulated in problem 2 and solved in problem 3, answer the following: a. What are the sensitivity ranges for the objective function coefficients? b. Determine the shadow prices for additional hours of production time on line 1 and line 2 hours. 5. Formulate and solve the model for the following problem: (Solver) Irwin Textile Mills produce two types of cotton cloth – denim and corduroy. Corduroy is a heavier grade of cotton cloth and as such requires 7.5 pounds of raw cotton per yard. Whereas denim requires 5 pounds of raw cotton per yard. A yard of corduroy requires 3.2 hours of processing time; a yard of denim requires 3.0 hours. Although the demand for denim is practically unlimited, the maximum demand for corduroy is 510 yards per month. The manufacturer has 6500 pounds of cotton and 3000 hours of processing time available each month. The manufacturer wants to know how many of each type of cloth to produce to maximize profit. Answer the following questions: a. How much extra cotton and processing time are left over at the optimal solution? Is the demand for corduroy met? b. What is the effect on the optimal solution if the profit per yard of denim is increased from $2.25 to $3.00? What is the effect of the profit per yard of corduroy is increased from $3.10 to $4.00? c. What would be the effect on the optimal solution if Irwin Mills could contain only 6000 pound of cotton per month? 6. Continuing the model from problem 5, answer the following: a. If Irwin Mills can obtain additional cotton or processing time, but not both, which should it select? How much? Explain your answer. b. Identify the sensitivity ranges for the objective function coefficients and for the constraint quantity values. Then explain the sensitivity range for the demand for corduroy. 7. United Aluminum Company of Cincinnati produces three grades (high, medium, and low) of aluminum at two mills. Each mill has a different production capacity (in tons per day) for each grade as follows: 	Aluminum Grade 	Mill 	 	1 	2 	High 	6 	2 	Medium 	2 	2 	Low 	4 	10 The company has contracted with a manufacturing firm to supply at least 12 tons of high-grade aluminum, and 5 tons of low-grade aluminum. It costs United $6000 per day to operate mill 1 and $7000 per day to operate mill 2. The company wants to know the number of days to operate each mill in order to meet the contract at minimum cost.  Formulate a linear programming model for this problem in “Standard Form”. 8. Solve the linear programming model formulated in problem 7 by using the computer and answer the following: a. Identify and explain the shadow prices for each of the aluminum grade contract requirements. b. Identify the sensitivity ranges for the objective function coefficients and the constraint quantity values. c. Would the solution values change if the contract requirements for high-grade aluminum were increased from 12 tons to 20 tons? If yes, what would the new solution values be? 9. The manager of a Burger Doodle franchise wants to determine how many sausage biscuits and ham biscuits to prepare each morning for breakfast customers to maximize profit. The two types of biscuits require the following resources: 	Biscuit 	Labor (hr.) 	Sausage (lb.) 	Ham (lb.) 	Flour (lb.) 	Sausage 	0.010 	0.10 	---- 	0.04 	Ham 	0.024 	---- 	0.15 	0.04 The franchise has 6 hours of labor available each morning. The manager has a contract with a local grocer for 30 pounds of sausage and 30 pounds of ham each morning. The manager also purchases 16 pounds of flour. The profit for a sausage biscuit is $0.60; the profit for a ham biscuit is $0.50. Formulate a linear programming model for this problem (Solver). 10. Solve the linear programming model developed for problem 9 by using the computer and answer the following questions: a. Identify and explain the shadow process for each of the resource constraints b. Which of the resources constrains profit the most? c. Identify the sensitivity ranges for the profit of a sausage biscuit and the amount of sausage available. Explain these sensitivity ranges.   P1 	Sporting Goods 	(a)		Resource Requirements per Unit				(b-1)		Resource Requirements per Unit 		Product	Rubber (lb.)	Leather (ft2)				Product	Rubber (lb.)	Leather (ft2) 		Basketball	3	4				Basketball	3	4 		Football	2	5				Football	2	5 					input Constraints 		Total resources available	500	800				Total resources available	500	800 			Basketball	Football					Basketball	Football 		Profits ($)	12	16				Profits ($)	13	16 		Basketball			Decision variables			Basketball 		Football						Football 		Maximized profits			Objective function			Maximized profits 	(b-2)		Resource Requirements per Unit				(C-1)		Resource Requirements per Unit 		Product	Rubber (lb.)	Leather (ft2)				Product	Rubber (lb.)	Leather (ft2) 		Basketball	3	4				Basketball	3	4 		Football	2	5				Football	2	5 					input Constraints 		Total resources available	500	800				Total resources available	1000	800 			Basketball	Football					Basketball	Football 		Profits ($)	12	15				Profits ($)	12	16 		Basketball			Decision variables			Basketball 		Football						Football 		Maximized profits			Objective function			Maximized profits 		Please use computer method to solve the problem					(C-2)		Resource Requirements per Unit 		Please enter your solution in Yellow cells						Product	Rubber (lb.)	Leather (ft2) 								Basketball	3	4 								Football	2	5 								Total resources available	500	1300 									Basketball	Football 								Profits ($)	12	16 					Decision variables			Basketball 								Football 					Objective function			Maximized profits P2 	A & B products 			Hours/ Unit 		Product	Line 1	Line2 		A	12	4 		B	4	8 					Constraints		Note: SUMPRODUCT(Col1, Col2) is a easier way to multiply 		Total Hours	60	40			two rows or two columns 			A	B			Standard Linear Programming:	Maximixe 	9 * A + 7 * B  		Profits ($)	9	7				Subject to	12 * A + 4 * B = 0 		Product B							B >= 0 		Maximized profits			Objective function P3 	A & B products 	(a)		Hours/ Unit			(b)		Hours/ Unit 		Product	Line 1	Line2			Product	Line 1	Line2 		A	12	4			A	12	4 		B	4	8			B	4	8 					Constraints 		Total Hours	60	40			Total Hours	40	40 			A	B				A	B 		Profits ($)	9	7			Profits ($)	9	7 		Product A			decision variables		Product A 		Product B					Product B 		Maximized profits			Objective function		Maximized profits 						(c-1)		Hours/ Unit 							Product	Line 1	Line2 							A	12	4 							B	4	8 							Total Hours	60	40 								A	B 							Profits ($)	9	15 							Product A 							Product B 							Maximized profits 						(c-2)		Hours/ Unit 							Product	Line 1	Line2 							A	12	4 							B	4	8 							Total Hours	60	40 								A	B 							Profits ($)	9	20 							Product A 							Product B 							Maximized profits P4 	Please run sensitivity analysis on P10 and enter the results (changes in coefficients of the objective function, and shadow prices) in YELLOW cells 		Sensitivity analysis	Min 	Max 		Product A			Coefficients in the objective function (profits for A and B) 		Product B 		Shadow price	Additional Profits 		Line 1 		Line 2 P5 	Irwin textile mills 	(a)		Corduroy	denim 		Profits for each product	3.1	2.25 					Resources		Available Resources	Left over 		Cotton	7.5	5		=	12 			Medium	2	2		>=	8	Please note, this constraint is missing in the problem 			Low	4	10		>=	5 			Aluminum Grade	Mill 				1	2 			Cost ($)	6000	7000 			Mill #1 			Mill #2 			Minimize Cost ($) 		a.       Identify and explain the shadow prices for each of the aluminum grade contract requirements. 				Shadow Price 			High 			Medium 			Low 		b.       Identify the sensitivity ranges for the objective function coefficients and the constraint quantity values. 				Min	Max 			Mill #1 			Mill #2 		c.	Aluminum Grade	Mill 				1	2	constraints 			High	6	2		>=	20 			Medium	2	2		>=	8 			Low	4	10		>=	5 			Aluminum Grade	Mill 				1	2 			Cost ($)	6000	7000 			Mill #1 			Mill #2 			Minimize Cost ($) P9 	Burger Doodle franchise  			Biscuit	Labor (hr.)	Sausage (lb.)	Ham (lb.)	Flour (lb.) 			Sausage 	0.01	0.1	---	0.04 			Ham	0.024	---	0.15	0.04 			Constraints 				6	30	30	16 				Sausage 	Ham 			Profits ($)	0.6	0.5 			Sausage  			Ham 			Maximize Profits

Rochak · Accepted Answer

P1
	Sporting Goods
	(a)		Resource Requirements per Unit				(b-1)		Resource Requirements per Unit
		Product	Rubber (lb.)	Leather (ft2)				Product	Rubber (lb.)	Leather (ft2)
		Basketball	3	4				Basketball	3	4
		Football	2	5				Football	2	5
			320	800	input Constraints				500	800
		Total resources available	500	800				Total resources available	500	800
			Basketball	Football					Basketball	Football
		Profits ($)	12	16				Profits ($)	13	16
		Basketball	0.00		Decision variables			Basketball	128.57
		Football	160.00					Football	57.14
		Maximized profits	2560.00		Objective function			Maximized profits	2585.71
	(b-2)		Resource Requirements per Unit				(C-1)		Resource Requirements per Unit
		Product	Rubber (lb.)	Leather (ft2)				Product	Rubber (lb.)	Leather (ft2)
		Basketball	3	4				Basketball	3	4
		Football	2	5				Football	2	5
			320	800	input Constraints				320	800
		Total resources available	500	800				Total resources available	1000	800
			Basketball	Football					Basketball	Football
		Profits ($)	12	15				Profits ($)	12	16
		Basketball	0.00		Decision variables			Basketball	0.00
		Football	160.00					Football	160.00
		Maximized profits	2400.00		Objective function			Maximized profits	2560.00
		Please use computer method to solve the problem					(C-2)		Resource Requirements per Unit
		Please enter your solution in Yellow cells						Product	Rubber (lb.)	Leather (ft2)
								Basketball	3	4
								Football	2	5
									500	1250
								Total resources available	500	1300
									Basketball	Football
								Profits ($)	12	16
					Decision variables			Basketball	0.00
								Football	250.00
					Objective function			Maximized profits	4000.

DSS610Quiz 4 Linear programming(NOTE: There is an Excel Spreadsheet available for these problems but for the ones asking for “Standard Form” hardcopy/manual layout and computation will be...

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