Question;MAT540;Week;7 Homework;Chapter 3;8.;Solve the model formulated in Problem 7 for Southern Sporting Goods Company;using the computer.;a.;State the optimal solution.;b.;What would be the effect on the optimal solution if the profit for a;basketball changed 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?;Reference Problem 7. Southern;Sporting Good 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 (lb.);Leather (ft2);Basketball;3;4;Football;2;5;Total resources available;500 lb.;800 ft2;10.;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;Line2;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.;11.;Solve problem 10 using the computer.;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?;c.;What would be the effect on the optimal solution if the profit for product;B was increased from $7 to $15 to $20?;12.;For the linear programming model formulated in Problem 10 and solved in;Problem 11.;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 and indicate whether the company would prefer additional line 1 or;line 2 hours.;14.;Solve the model formulated in Problem 13 for Irwin Textile Mills.;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 if 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 Mils could obtain;only 6,000 pounds of cotton per month?;Reference Problem 13. Irwin;Textile Mills produces 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 6,500 pounds of cotton and 3,000 hours of processing time available each;month. The manufacturer makes a profit;of $2.25 per yard of denim and $3.10 per yard of corduroy. The manufacturer wants to know how many yards;of each type of cloth to produce to maximize profit. Formulate the model and put it into standard;form. Solve it.;15.;Continuing the model from Problem 14.;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.;16.;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 $6,000 per day to operate mill 1 and $7,000 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.;a. Formulate a linear;programming model for this problem.;18.;Solve the linear programming model formulated in Problem 16 for Unite;Aluminum Company by using the computer.;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 alumimum were increased from 12 tons to 20 tons? If yes, what would the new solution values;be?;24.;Solve the linear programming model developed in Problem 22 for the Burger;Doodle restaurant by using the computer.;a.;Identify and explain the shadow prices 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.;Reference Problem 22. The;manager of a Burger Doodle franchise wants to determine how many sausage;biscuits and ham biscuits to prepare each morning for breakfast customers. 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. The manager wants to know the number of each;type of biscuit to prepare each morning in order to maximize profit. Formulate a linear programming model for this;problem.
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