ABC Products Produces Three Products (A, B and C) on Three

ABC Products produces three products (A, B and C) on three machines. Machines 1 and 2 are available for 40 hours a week and Machine 3 is available for 60 hours a week. Profit contribution and standard production time in hours are given in the following table:
$\begin{array}{cccc}&&\text {Product}\\& \underline{\text {A}}& \underline{\text {B}}&\underline{\text {C}}\\\text { Profit Contribution/Unit } & \$ 40 & \$ 60 & \$ 30 \\\text { Machine } \# 1 \text { time/unit) } & 0.6 & 2.2 & 1.8 \\\text { Machine } \# 2 \text { time/unit) } & 1.2 & 0.8 & 0.7 \\\text { Machine } \# 3 \text { time/unit) } & 2.4 & 2.8 & 2.0\end{array}$

Only one operator per machine is required on Machines #1 and #2. Two operators are required for Machine #3. Therefore, two hours of labor must be scheduled for each hour of Machine #3's time. To restate this requirement, two operators must be scheduled for each hour of Machine #3's operation, as well as one operator for each hour of Machine #1's operation and one operator for each hour of Machine #2's operation. A total of 110 labor hours is available for assignment to the three machines during the coming week. Other production requirements are that Product A cannot account for more than 40% of the units produced and that Product C must account for at least 25% of the units produced.
a. Develop the constraint for the capacity limit of Machine #1.
b. Develop the constraint for the capacity limit of Machine #3.
c. Develop the constraint for the labor capacity limit.
d. Develop the constraint for limiting Product A to no more than 40% of the units produced.
e. Develop the constraint that ensures Product C accounts for at least 25% of the units produced.