The Supervisor of a Manufacturing Plant Is Trying to Determine

The supervisor of a manufacturing plant is trying to determine how many of two parts, Part X and Part Y, are to be produced per day. Each part must be processed in three sections of the plant. The time required for the production along with the profit contribution for each part are given in the following table. $$\begin{array}{l}\begin{array} { l c c c c } &&&\text { Time required (Minutes/Unit) }\\& \text { Section 1 } & \text { Section 2 } & \text { Section 3 } & \text { Profit/Unit } \\\hline \text { Part X } & 50 & 30 & 18 & \$ 2 \\\text { Part Y } & 80 & 45 & 22 & \$ 3 \\\text { Available time (minutes) } & 3600 & 2500 & 1200 &\end{array}\end{array}$$ No more than 60 units of Part X and up to 70 units of Part Y can be produced per day. The company already has orders for 30 units of Part Y that must be satisfied.
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a. Develop a linear programming model and solve the model to determine the optimal production quantities of Parts X and Y.
b. If more time could be made available in Section 2, how much would the profit increase? (Hint: Generate Answer Report).