Volimer Manufacturing makes three components for sale to refrigeration companies. The components are processed on two machines: a shaper and a grinder. The times (in minuter) required on each machine are as follons. \begin{tabular}{|c|c|c|} \hline & \multicolumn{2}{|c|}{ Machine } \\ \hline Compenent & Shaper & Grinder \\ \hline 1 & 6 & 4 \\ \hline 2 & 4 & 5 \\ \hline 3 & 4 & 2 \\ \hline \end{tabular} The shaper is availabie for 120 hours, and the grinder is available for 110 hours. No more than 200 units of component 3 can be sold, but up to a00 units of each of the ocher cimponents can be sold. In foct, the company already has orders for 600 units of component 1 that must be satisfied. The per unit seiling price and per unit variabie costs for each of the three components are as follows. \begin{tabular}{|c|c|c|c|} \hline Campanent & Selling Price & Material Cost & Labor Cost \\ \hline 1 & $25 & $12 & $5 \\ \hline 2 & $18 & $8 & $4 \\ \hline 3 & $27 & $13 & $5 \\ \hline \end{tabular} (a) For evch componeri, catculate the profit margin (in dollars, profit margin - selling grice - matenal cast - labor cost), farmulate and solve for the recommended production quaskities that will maximize contribution to profi. componert 1 unts component 2 unsts Volimer 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. The shaper is availablo for 120 hours, and the grinder is available for 110 hours. No more than 200 units of component 3 can be sold, but up to 800 units of each of the other componi can be sold. in fact, the company already has orders for 600 units of 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. (a) For each component, calculate the profit margin (in dollars, profit margin = selling price material cost labor cost). cempenent 14 component 2 companent 3 Formulate and solve for the recommended preduction quantities that will maximize contribution to profit. component 1 component 2 units component 3 units Lnits (b) What are the objective coefficient manges (in dollars) for the three components? (If there is no upper or lower limit, enter No LimII. Round your answers to two decimal placus.) (b) What are the objective coefficient ranges (in dollars) for the three components? (If there is no upper or lower limit, enter NO LIMIT, Round your answers to two decimal- Interpret these ranges for company management. Individual changes in the profit coefficients within these ranges will not cause a change in the optimal number of components to produce. Individual changes in the profit coefficients within these ranges will cause changes in the optimal number of components to produce. Individual changes in the profit coefficients outside these ranges will not cause a change in the optimal number of components to produce. (c) What are the right-hand-side ranges? (Use minutes for time. If there is no upper or lower limit, enter No LIMIT. Round your answers to the nearest integer.) shaper aveilability grinder avaitablity Interpret these ranges for company management. These are the ranges over which the shadow prices for the associated constraints are not applicable. These are the ranges over which the shadow prices for the associated constraints are applicable. These are the ranges over which the reduced costs for the associated constraints are not applicable. These are the ranges over which the reduced costs for the associated constraints are applicable. (d) If more time could be made available on the grinder, how mueh would it be worth? Every additional minate on the grinder increases profits by $1.50. Nothing, since there are 300 minutes of slack time on the grinder at the optimal solution. Cvery additional minute on the grinder increases profits by $3. Every additional minute on the grinder decreases profits by $1 These are the ranges over which the reduced costs for the associated constraints are applicable. (d) If more time could be made available on the grinder, how much would it be worth? Every additional minute on the grinder increases profits by $1.50. Nothing, since there are 300 minutes of slack time on the grinder at the optimal solution. Every additional minute on the grinder increases profits by $3. Every additional minute on the grinder decreases profits by $1. (e) If more units of component 3 can be sold by reducing the sales price by $4, should the company reduce th Yes. At that price, the optimal solution would produce 700 units of component 3. Yes. Every additional unit of component 3 increases profits by $3. No. There is a slack of 300 units so selling more would not improve profits. No. At that price, the optimal solution would not produce any of component 3
