Question 2 The Hot Dawg Company (HDC) must determine the quantities of beef, chicken, and lamb...

 
 

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Question 2 The Hot Dawg Company (HDC) must determine the quantities of beef, chicken, and lamb to use in blending 100 pounds of its Super Sausage. In blending the Super Sausage, HDC must meet the following four product requirements: 1. The percentage of the sausage's weight that is protein must be at least 12%. 2. The percentage of the sausage's weight that is fat must be at most 24%. 3. The percentage of the sausage's weight that is water must be at most 64%. 4. The percentage of the sausage's weight that is lamb must be at least 30%. The table below provides the composition and cost per pound of each type of meat. Beef Chicken Lamb 20 15 15 20 15 25 Percent protein Percent fat Percent water Cost per pound 60 70 60 $1.00 $0.50 $0.70 Assume that spices and casings contribute an insignificant amount to the total sausage weight and that unlimited quantities of beef, chicken, and lamb are available to HDC at the indicated costs. Let x, xc and x, denote the respective pounds of beef, chicken and lamb used to blend the 100 pounds of Super Sausage. The LP formulation for determining the blend that satisfies HDC's product requirements at minimum cost is as follows. Minimize XB +0.5xc +0.7x₁ subject to XB + Xc + x₁ = 100 0.2x +0.15xc +0.15x₁ 212 0.2x +0.15xc +0.25x, ≤24 0.6x +0.7x +0.6.x, ≤ 64 x₁ ≥ 30 XB XC , X₁ 20 (1) You are required to input the LP formation into Excel, and use Excel Solver to solve the problem. In your answer, please print out and attach the Formulation at the optimal solution, Answer Report, and Sensitivity Report, similar to those in the lecture notes. (16 marks) Parts (ii) - (vii) below request you to use the computer output in part (i) to analyse the effect of a change in a decision variable's objective function coefficient or a structural constraint's right-hand side. Regard each part as independent of the other parts. In some parts, the computer output may provide insufficient information to allow you to answer, in which case you should state "Insufficient information!" (ii) Write down the optimal values of the decision variables and the minimum total cost. (4 marks) (iii) If the cost per pound of lamb increases from $0.70 to $0.95, what are the optimal values of the decision variables and the minimum total cost? (6 marks) (iv) If the cost per pound of beef decreases from $1.00 to $0.65, what are the optimal values of the decision variables and the minimum total cost? (6 marks) (v) If the maximum fat content decreases from 24% to 20%, what is the minimum total cost? (6 marks) (vi) If the maximum water content decreases from 64% to 62%, what is the minimum total cost? (6 marks) (vii) If HDC must blend 90 pounds of Super Sausage instead of 100 pounds, what is the minimum total cost? (6 marks) Question 2 The Hot Dawg Company (HDC) must determine the quantities of beef, chicken, and lamb to use in blending 100 pounds of its Super Sausage. In blending the Super Sausage, HDC must meet the following four product requirements: 1. The percentage of the sausage's weight that is protein must be at least 12%. 2. The percentage of the sausage's weight that is fat must be at most 24%. 3. The percentage of the sausage's weight that is water must be at most 64%. 4. The percentage of the sausage's weight that is lamb must be at least 30%. The table below provides the composition and cost per pound of each type of meat. Beef Chicken Lamb 20 15 15 20 15 25 Percent protein Percent fat Percent water Cost per pound 60 70 60 $1.00 $0.50 $0.70 Assume that spices and casings contribute an insignificant amount to the total sausage weight and that unlimited quantities of beef, chicken, and lamb are available to HDC at the indicated costs. Let x, xc and x, denote the respective pounds of beef, chicken and lamb used to blend the 100 pounds of Super Sausage. The LP formulation for determining the blend that satisfies HDC's product requirements at minimum cost is as follows. Minimize XB +0.5xc +0.7x₁ subject to XB + Xc + x₁ = 100 0.2x +0.15xc +0.15x₁ 212 0.2x +0.15xc +0.25x, ≤24 0.6x +0.7x +0.6.x, ≤ 64 x₁ ≥ 30 XB XC , X₁ 20 (1) You are required to input the LP formation into Excel, and use Excel Solver to solve the problem. In your answer, please print out and attach the Formulation at the optimal solution, Answer Report, and Sensitivity Report, similar to those in the lecture notes. (16 marks) Parts (ii) - (vii) below request you to use the computer output in part (i) to analyse the effect of a change in a decision variable's objective function coefficient or a structural constraint's right-hand side. Regard each part as independent of the other parts. In some parts, the computer output may provide insufficient information to allow you to answer, in which case you should state "Insufficient information!" (ii) Write down the optimal values of the decision variables and the minimum total cost. (4 marks) (iii) If the cost per pound of lamb increases from $0.70 to $0.95, what are the optimal values of the decision variables and the minimum total cost? (6 marks) (iv) If the cost per pound of beef decreases from $1.00 to $0.65, what are the optimal values of the decision variables and the minimum total cost? (6 marks) (v) If the maximum fat content decreases from 24% to 20%, what is the minimum total cost? (6 marks) (vi) If the maximum water content decreases from 64% to 62%, what is the minimum total cost? (6 marks) (vii) If HDC must blend 90 pounds of Super Sausage instead of 100 pounds, what is the minimum total cost? (6 marks)

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Answer i Xb Xc Xl Obj ... View the full answer