A Firm Has 4 Plants That Produce Widgets The Firm Needs to Satisfy All Demand Each Day, but B

question 52

Multiple Choice

A firm has 4 plants that produce widgets. Plants A, B, and C can each produce 100 widgets per day. Plant D can produce 50 widgets per day. Each day, the widgets produced in the plants must be shipped to satisfy the demand of 3 customers. Customer 1 requires 75 units per day, customer 2 requires 100 units per day, and customer 3 requires 175 units per day. The shipping costs for each possible route are shown in the table below:
$\begin{array}{c}Shipping~ Costs&&&Customer\\per~unit~Plant&&1&2&3\\\mathrm{A} && \$ 25 & \$ 35 & \$ 15 \\\mathrm{~B} && \$ 20 & \$ 30 & \$ 40 \\\mathrm{C} && \$ 40 & \$ 35 & \$ 20 \\\mathrm{D} && \$ 15 & \$ 20 & \$ 25\end{array}$
The firm needs to satisfy all demand each day, but would like to minimize the total costs.
Which of the following constraints is unnecessary for this problem (xi,j is the number of widgets shipped from factory i to customer j) ?

• A) xA,1 + xA,2 + xA,3 ? 100
• B) xB,1 + xB,2 + xB,3 ? 100
• C) xC,1 + xxC,2 + xxC,3 ? 100
• D) xA,1 + xB,1 + xxC,1 ? 75
• E) xA,1, xA,2, xA,3, xB,1, xB,2, xB,3, xC,1, xC,2, xC,3 integer

---

Definitions:

Conversion Costs

The sum of direct labor and manufacturing overhead costs, representing the costs incurred to convert raw materials into finished products.

First-In, First-Out

A rephrased definition: An accounting method used to value inventory and calculate cost of goods sold, assuming the earliest goods purchased are the first to be sold.

Conversion Costs

Conversion costs are the costs required to convert raw materials into finished products, including labor and overhead.

Factory Overhead

Expenses related to the operation of a manufacturing plant that are not directly tied to a specific product, including utilities, depreciation, and facility maintenance.