A company makes two models of doghouses. The times (in hours) required for assembling, painting, and packaging are shown in the table. $\begin{array} { l l l }
\text { Process } & \text { Model A } & \text { Model B } \
\text { Assembling } & 2.5 & 3 \
\text { Painting } & 2 & 1 \
\text { Packaging } & 0.75 & 1.25
\end{array}$ The total times available for assembling, Painting, and packaging are 4000 hours, 2500 hours, and 1500 hours, respectively. The profits per unit are $60 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 occurs when 571 units of model A and 857 units of model B are produced. The optimal profit is $98,571.
B)The optimal profit occurs when 571 units of model A and 857 units of model B are produced. The optimal profit is $98,535.
C)The optimal profit occurs when 571 units of model A and 857 units of model B are produced. The optimal profit is $97,500.
D)The optimal profit occurs when 571 units of model A and 857 units of model B are produced. The optimal profit is $90,000.
E)The optimal profit occurs when 571 units of model A and 857 units of model B are produced. The optimal profit is $75,000.

Question

A company makes two models of doghouses. The times (in hours) required for assembling, painting, and packaging are shown in the table. $\begin{array} { l l l } 
\text { Process } & \text { Model A } & \text { Model B } \
\text { Assembling } & 2.5 & 3 \
\text { Painting } & 2 & 1 \
\text { Packaging } & 0.75 & 1.25
\end{array}$ The total times available for assembling, Painting, and packaging are 4000 hours, 2500 hours, and 1500 hours, respectively. The profits per unit are $60 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 occurs when 571 units of model A and 857 units of model B are produced. The optimal profit is $98,571.
B)The optimal profit occurs when 571 units of model A and 857 units of model B are produced. The optimal profit is $98,535.
C)The optimal profit occurs when 571 units of model A and 857 units of model B are produced. The optimal profit is $97,500.
D)The optimal profit occurs when 571 units of model A and 857 units of model B are produced. The optimal profit is $90,000.
E)The optimal profit occurs when 571 units of model A and 857 units of model B are produced. The optimal profit is $75,000.

Quizplus · Accepted Answer

The optimal production levels and profit can be determined by setting up and solving a linear programming problem with the given constraints (time for assembling, painting, and packaging) and the objective function (maximizing profit). The correct answer involves calculating the total profit based on the production levels of model A and model B, which are given as 571 and 857 units, respectively. The profit for each model is calculated by multiplying the number of units by the profit per unit ($60 for model A and $75 for model B). The total profit is the sum of these individual profits, which matches the value provided in option B.

A Company Makes Two Models of Doghouses The Total Times Available for Assembling, Painting, and Packaging Are