There are two products to produce. The unit profit of product 1 is 4 and that...

      

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There are two products to produce. The unit profit of product 1 is 4 and that of product 2 is 2. Two resources are required. They are labor hours and key components. Each product 1 will consume 2 units of labor hours and 3 key components. Each product 2 will consume 4 units of labor hours and 5 key components. The availability of labor hours is 20 units and that of key components is 15. The company wants to maximize its profits. Implement the following LP problem in Excel. Use Solver to solve the problem and create a Sensitivity Report. Use this information to answer the following questions: Variable: X1: Number of product 1 to produce X2: Number of product 2 to produce Max 4X1+2X2 Subject to: 2X1+4X2<=20 (Labor Hour) 3X1+5X2<=15 (Key Components) Non-negativity What is the optimal solution? O A. X1=5, X2%3D0 O B. X1=0, X2=0 O C.X1=0, X2=5 O D.X1=5, X2=5 Sensitivity Report Variable Cells Final Reduced Objective Allowable Allowable Cell Name Value Cost Coefficient Increase Decrease SAS2 X1 4 1E+30 2.8 $B$2 X2 -4.6667 2 4.6667 1E+30 Constraints Final Shadow Constraint Allowable Allowable Cell Name Value Price R.H. Side Increase Decrease SC$4 LHS 10 ????? 20 1E+30 ????? SC$5 LHS 15 1.3333 15 15 15 Which value can the unit profit of product 1 be without changing the optimal solution? O A. 0.2 B. 1000 ОС.1.1 O D. 0.8 Which statement regarding the shadow price of the Labor Hour constraint is true? O A. The shadow price of the first constraint is zero because the shadow price of a slack constraint is always 0. B. The shadow price of the first constraint is negative because the shadow price of a slack constraint is always negative. OC.There is no way to know about the shadow price of the first constraint without the sensitivity report. D. The shadow price of the first constraint is positive because the shadow price of a slack constraint is always positive. What is the optimal objective function value if key component availability changes from 15 to 25? O A. 16.6667 B. 33.3333 OC.6.6667 D. 35.3333 What is the reduced cost of product 2 if it only needs 1 key component? O A. -0.6667 O B. 0 C.-1.3333 O D. 0.6667 If product 2 only need 1 key component instead of 5, which statement is true? O A. It will not be worthwhile to produce product 2 because the reduced cost will be positive. B. It will be worthwhile to produce product 2 because the reduced cost will be positive. O C.It will be worthwhile to produce product 2 because the reduced cost will be negative. O D. It will not be worthwhile to produce product 2 because the reduced cost will be zero. There are two products to produce. The unit profit of product 1 is 4 and that of product 2 is 2. Two resources are required. They are labor hours and key components. Each product 1 will consume 2 units of labor hours and 3 key components. Each product 2 will consume 4 units of labor hours and 5 key components. The availability of labor hours is 20 units and that of key components is 15. The company wants to maximize its profits. Implement the following LP problem in Excel. Use Solver to solve the problem and create a Sensitivity Report. Use this information to answer the following questions: Variable: X1: Number of product 1 to produce X2: Number of product 2 to produce Max 4X1+2X2 Subject to: 2X1+4X2<=20 (Labor Hour) 3X1+5X2<=15 (Key Components) Non-negativity What is the optimal solution? O A. X1=5, X2%3D0 O B. X1=0, X2=0 O C.X1=0, X2=5 O D.X1=5, X2=5 There are two products to produce. The unit profit of product 1 is 4 and that of product 2 is 2. Two resources are required. They are labor hours and key components. Each product 1 will consume 2 units of labor hours and 3 key components. Each product 2 will consume 4 units of labor hours and 5 key components. The availability of labor hours is 20 units and that of key components is 15. The company wants to maximize its profits. Implement the following LP problem in Excel. Use Solver to solve the problem and create a Sensitivity Report. Use this information to answer the following questions: Variable: X1: Number of product 1 to produce X2: Number of product 2 to produce Max 4X1+2X2 Subject to: 2X1+4X2<=20 (Labor Hour) 3X1+5X2<=15 (Key Components) Non-negativity What is the optimal solution? O A. X1=5, X2%3D0 O B. X1=0, X2=0 O C.X1=0, X2=5 O D.X1=5, X2=5 Sensitivity Report Variable Cells Final Reduced Objective Allowable Allowable Cell Name Value Cost Coefficient Increase Decrease SAS2 X1 4 1E+30 2.8 $B$2 X2 -4.6667 2 4.6667 1E+30 Constraints Final Shadow Constraint Allowable Allowable Cell Name Value Price R.H. Side Increase Decrease SC$4 LHS 10 ????? 20 1E+30 ????? SC$5 LHS 15 1.3333 15 15 15 Which value can the unit profit of product 1 be without changing the optimal solution? O A. 0.2 B. 1000 ОС.1.1 O D. 0.8 Sensitivity Report Variable Cells Final Reduced Objective Allowable Allowable Cell Name Value Cost Coefficient Increase Decrease SAS2 X1 4 1E+30 2.8 $B$2 X2 -4.6667 2 4.6667 1E+30 Constraints Final Shadow Constraint Allowable Allowable Cell Name Value Price R.H. Side Increase Decrease SC$4 LHS 10 ????? 20 1E+30 ????? SC$5 LHS 15 1.3333 15 15 15 Which value can the unit profit of product 1 be without changing the optimal solution? O A. 0.2 B. 1000 ОС.1.1 O D. 0.8 Which statement regarding the shadow price of the Labor Hour constraint is true? O A. The shadow price of the first constraint is zero because the shadow price of a slack constraint is always 0. B. The shadow price of the first constraint is negative because the shadow price of a slack constraint is always negative. OC.There is no way to know about the shadow price of the first constraint without the sensitivity report. D. The shadow price of the first constraint is positive because the shadow price of a slack constraint is always positive. What is the optimal objective function value if key component availability changes from 15 to 25? O A. 16.6667 B. 33.3333 OC.6.6667 D. 35.3333 What is the reduced cost of product 2 if it only needs 1 key component? O A. -0.6667 O B. 0 C.-1.3333 O D. 0.6667 Which statement regarding the shadow price of the Labor Hour constraint is true? O A. The shadow price of the first constraint is zero because the shadow price of a slack constraint is always 0. B. The shadow price of the first constraint is negative because the shadow price of a slack constraint is always negative. OC.There is no way to know about the shadow price of the first constraint without the sensitivity report. D. The shadow price of the first constraint is positive because the shadow price of a slack constraint is always positive. What is the optimal objective function value if key component availability changes from 15 to 25? O A. 16.6667 B. 33.3333 OC.6.6667 D. 35.3333 What is the reduced cost of product 2 if it only needs 1 key component? O A. -0.6667 O B. 0 C.-1.3333 O D. 0.6667 If product 2 only need 1 key component instead of 5, which statement is true? O A. It will not be worthwhile to produce product 2 because the reduced cost will be positive. B. It will be worthwhile to produce product 2 because the reduced cost will be positive. O C.It will be worthwhile to produce product 2 because the reduced cost will be negative. O D. It will not be worthwhile to produce product 2 because the reduced cost will be zero. If product 2 only need 1 key component instead of 5, which statement is true? O A. It will not be worthwhile to produce product 2 because the reduced cost will be positive. B. It will be worthwhile to produce product 2 because the reduced cost will be positive. O C.It will be worthwhile to produce product 2 because the reduced cost will be negative. O D. It will not be worthwhile to produce product 2 because the reduced cost will be zero.

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Solving the given formulation in Excel we get the below solution and the Sensitivity Report The sens... View the full answer