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

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Definitions:

Merchandise Inventory

Goods a company has in stock and available for sale, typically in a retail or wholesale setting.

Inventory Shrinkage

The loss of products between purchase and sale, often due to theft, damage, or errors in counting.

Physical Count

The process of counting the actual number of items in inventory, typically to verify accounting records or when preparing financial statements.

Net Method

An accounting method that records purchases at the net price after deduction of any purchase discounts.