A Coffee Manufacturing Company Has Two Processing Plants (P1 and P2)

question 25

Essay

A coffee manufacturing company has two processing plants (P1 and P2) that roast imported coffee beans. After roasting, the plants produce three types of coffee beans, A, B, and C. The company has contracted with a chain of cafes to provide coffee beans each week in the following quantities - 20 tons of type A, 11 tons of type B, and 18 tons of type C. The two plants have the same capacity, but their diverse operational procedures affect costs per ton as below.
​ $$\begin{array} { l c c c c } & { \text { Manufacturing Cost per Ton (\$) } } & \\\hline \text { Plant } & \text { A } & \text { B } & \text { C } & \text { Capacity } \\\hline \text { P1 } & 900 & 1125 & 875 & 25 \\\text { P2 } & 850 & 1200 & 950 & 25 \\\text { Demand } & 20 & 11 & 18 &\end{array}$$ ​
Formulate and solve the all-integer model that will determine how many tons of each type of coffee beans are produced in each plant while minimizing the total cost.

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Definitions:

Income

A measure of money received by an individual or household over a certain period of time, typically earned through work, investments, or other sources.

Price

The amount of money required to purchase a product or service, typically determined by supply and demand dynamics.

Marginal Rate

The rate at which one quantity changes with respect to a change in another, at the margin, especially in the context of cost or tax.

Utility Function

A representation in economics of how a consumer ranks different bundles of goods based on the level of satisfaction (utility) each bundle provides.