A Computer Manufacturing Company Wants to Develop a Monthly Plan

question 42

Essay

A computer manufacturing company wants to develop a monthly plan for shipping finished products from three of its manufacturing facilities to three regional warehouses. It is thinking about using a transportation LP formulation to exactly match capacities and requirements. Data on transportation costs in dollars per unit), capacities, and requirements are given below:
$$\begin{array} { c c c c c } & \text { Plant } & \text { Plant } & \text { Plant } & \\\underline { \text { Warehouse} } & 1 & \underline { 2 } & \underline { 3 } & \underline { \text { Requirements } }\\\mathbf { x } & 2 . \overline { 4 } 1 & 1 . \overline { 6 } 3 & \text { 2.09 } & 8,000 \\Y & 3.18 & 5.62 & 1.74 & 2,000 \\\text { Z } & 4.12 & 3.16 & \text { 3.0 } & 3,000 \\ \text { Capacities } & 4,000 & 0,000 & 3,000 & \\\end{array}$$
a. How many variables are involved in the LP formulation?
b. How many constraints are there in this problem?
c. What is the constraint corresponding to plant 2?

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Definitions:

Perfectly Competitive

Describes a market structure where many firms offer homogeneous products, and no single buyer or seller can influence the market price.

Long-Run Equilibrium

A state in an economy or market where all factors of production are fully employed and economic forces are in balance, persisting over a long period.

MR = MC

A condition in economics where marginal revenue equals marginal cost; it's the optimal production point for firms maximizing their profit.

Monopolistically Competitive

Refers to a market structure where many companies sell products that are similar but not identical, allowing for some degree of market power and product differentiation.