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

question 25

Essay

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.

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Definitions:

Mass Services

Services that are provided on a large scale, aiming at a broad customer base, often standardized for efficiency.

Upstream Activity

Refers to the initial stages in the production process, often including exploration and extraction in industries like oil and gas.

Value Chain

The series of steps that a company takes to create or add value to a product, from raw materials to finished product.

Financial Planning Business

A service-oriented business that provides personalized financial advice, including investment management, income planning, and tax strategies, to help clients achieve their financial goals.