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:

Positive Externality

A beneficial effect experienced by a third-party or the society at large, as a result of an economic activity, that isn't reflected in the cost.

Garden

A planned space, usually outdoors, set aside for the display, cultivation, and enjoyment of plants and other forms of nature.

Pizza Delivered

A service where a pizza is prepared, baked, and brought to the customer's location by a restaurant or pizzeria.

Smokestack Scrubbers

Pollution control devices installed in smokestacks to remove or neutralize harmful substances from exhaust gases.