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

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.