A manufacturer produces two models of bicycles. The times (in hours) required for assembling, painting, and packaging each model are shown in the table. $\begin{array} { l l l }
\text { Process } & \text { Model A } & \text { Model B } \
\text { Assembling } & 2 & 2.5 \
\text { Painting } & 4 & 1 \
\text { Packaging } & 1 & 0.75
\end{array}$ The total times available for assembling, painting, and packing are 4000 hours, 4800 hours, and 1500 hours, respectively. The profit per unit are $50 for model A and $75 for model B. What is the optimal production level for each model? What is the optimal profit?
A)The optimal profit of $120,000 occurs when no units of model A and 1600 units of of model B are produced.
B)The optimal profit of $112,000 occurs when no units of model A and 1000 units of of model B are produced.
C)The optimal profit of $97,500 occurs when no units of model A and 600 units of of model B are produced.
D)The optimal profit of $60,000 occurs when no units of model A and 0 units of of model B are produced.
E)The optimal profit of $112,000 occurs when no units of model A and 750 units of of model B are produced.

Question

A manufacturer produces two models of bicycles. The times (in hours) required for assembling, painting, and packaging each model are shown in the table. $\begin{array} { l l l } 
\text { Process } & \text { Model A } & \text { Model B } \
\text { Assembling } & 2 & 2.5 \
\text { Painting } & 4 & 1 \
\text { Packaging } & 1 & 0.75
\end{array}$ The total times available for assembling, painting, and packing are 4000 hours, 4800 hours, and 1500 hours, respectively. The profit per unit are $50 for model A and $75 for model B. What is the optimal production level for each model? What is the optimal profit?
A)The optimal profit of $120,000 occurs when no units of model A and 1600 units of of model B are produced.
B)The optimal profit of $112,000 occurs when no units of model A and 1000 units of of model B are produced.
C)The optimal profit of $97,500 occurs when no units of model A and 600 units of of model B are produced.
D)The optimal profit of $60,000 occurs when no units of model A and 0 units of of model B are produced.
E)The optimal profit of $112,000 occurs when no units of model A and 750 units of of model B are produced.

Quizplus · Accepted Answer

The optimal production level and profit can be determined by setting up and solving a linear programming problem. Given the constraints on assembling, painting, and packaging times, and the profit per unit for each model, the solution maximizes profit. The constraints can be represented as inequalities based on the available hours for each process and the time required per unit for each model. Solving this optimization problem, option A provides the highest profit, indicating that focusing production solely on Model B to its maximum capacity under the given constraints yields the optimal outcome.

A Manufacturer Produces Two Models of Bicycles The Total Times Available for Assembling, Painting, and Packing Are