Vollmer Manufacturing makes three components for sale to refrigeration companies. The components are processed on two machines: a shaper and a grinder. The times (in minutes) required on each machine are as follows: Machine Component Shaper Grinder 6 4 2 4 5 The shaper is available for 120 hours, and the grinder for 110 hours. No more than 200 units f component 3 can be sold, but up to 1,000 units of component 1 and up to 1,000 units of component 2 can be sold. In fact, the company already has orders for 600 units component 1 that must be satisfied. The per unit selling price and per unit variable costs for each of the three components are as follows: Component Selling price Material Cost Labor Cost 1 $25 $12 2 3 $18 $27 $8 $5 $4 $13 $5 (a) For each component, calculate the profit margin (profit margin = selling price - material cost Component 1: $ 600 Component 2: $ 700 Component 3: $ 200 labor cost). Formulate and solve the model to determine the maximum profit. If the constant is "1", it must be entered in the box. If an amount is zero, enter "0". Let C1 units of component 1 manufactured C2 = units of component 2 manufactured C3 = units of component 3 manufactured Max $ 8 6 C₂ 9 G₂ s.t. Maximum profit: $ * C₁ × Ct + * C₁ C1, C2, C3 × G × Select your answer- * Shaper Select your answer- Grinder Maximum units of component Select your answer 3 Maximum units of component Select your answer - 1 × Maximum units of component Select your answer 2 Minimum units of component Select your answer - 1 × Select your answer (b) What are the objective coefficients ranges for the three components? required, round your answers to two decimal places. Variable Objective Coefficient Range × C1 -Select your answer- Select your answer - V C₂ -Select your answer- to Select your answer × C3 -Select your answer- to - Select your answer Interpret these ranges for company management. Individual changes in the profit coefficients - Select your answer - (c) What are the right-hand-side ranges? these ranges will not cause a change in the optimal number of components to produce. Constraint Right-Hand-Side Range 1 -Select your answer - V to -Select your answer- x 2 - Select your answer - ✓ Interpret these ranges for company management. to - Select your answer - These are the ranges over which the shadow prices for the associated constraints - Select your answer - applicable. (d) If more time could be made available on the grinder, how much would it be worth? Explain. - Select your answer - V, because the constraint related to the time available on the grinder - Select your answer - binding. (e) If more units f component 3 can be sold by reducing the sales price by $4, should the company reduce the price? - Select your answer - , because the production of component 3 would be -Select your answer- profitable than the production of the other two components and at the reduced price - Select your answer - of component 3 would be produced.

Vollmer Manufacturing makes three components for sale to refrigeration companies. The components are processed on two machines: a shaper and a grinder. The times (in minutes) required on each machine are as follows: Machine Component Shaper Grinder 6 4 2 4 5 The shaper is available for 120 hours, and the grinder for 110 hours. No more than 200 units f component 3 can be sold, but up to 1,000 units of component 1 and up to 1,000 units of component 2 can be sold. In fact, the company already has orders for 600 units component 1 that must be satisfied. The per unit selling price and per unit variable costs for each of the three components are as follows: Component Selling price Material Cost Labor Cost 1 $25 $12 2 3 $18 $27 $8 $5 $4 $13 $5 (a) For each component, calculate the profit margin (profit margin = selling price - material cost Component 1: $ 600 Component 2: $ 700 Component 3: $ 200 labor cost). Formulate and solve the model to determine the maximum profit. If the constant is "1", it must be entered in the box. If an amount is zero, enter "0". Let C1 units of component 1 manufactured C2 = units of component 2 manufactured C3 = units of component 3 manufactured Max $ 8 6 C₂ 9 G₂ s.t. Maximum profit: $ * C₁ × Ct + * C₁ C1, C2, C3 × G × Select your answer- * Shaper Select your answer- Grinder Maximum units of component Select your answer 3 Maximum units of component Select your answer - 1 × Maximum units of component Select your answer 2 Minimum units of component Select your answer - 1 × Select your answer (b) What are the objective coefficients ranges for the three components? required, round your answers to two decimal places. Variable Objective Coefficient Range × C1 -Select your answer- Select your answer - V C₂ -Select your answer- to Select your answer × C3 -Select your answer- to - Select your answer Interpret these ranges for company management. Individual changes in the profit coefficients - Select your answer - (c) What are the right-hand-side ranges? these ranges will not cause a change in the optimal number of components to produce. Constraint Right-Hand-Side Range 1 -Select your answer - V to -Select your answer- x 2 - Select your answer - ✓ Interpret these ranges for company management. to - Select your answer - These are the ranges over which the shadow prices for the associated constraints - Select your answer - applicable. (d) If more time could be made available on the grinder, how much would it be worth? Explain. - Select your answer - V, because the constraint related to the time available on the grinder - Select your answer - binding. (e) If more units f component 3 can be sold by reducing the sales price by $4, should the company reduce the price? - Select your answer - , because the production of component 3 would be -Select your answer- profitable than the production of the other two components and at the reduced price - Select your answer - of component 3 would be produced.

Practical Management Science

6th Edition

ISBN:9781337406659

Author:WINSTON, Wayne L.

Publisher:WINSTON, Wayne L.

Chapter4: Linear Programming Models

Section: Chapter Questions

Problem 111P

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