A coffee manufacturing company has two different plants 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 per week, 20 tons of coffee bean A, 11 tons of coffee bean B, and 18 tons of coffee bean C. The two plants have the same capacity, but diverse operational features as below:
Manufacturing Cost per Ton ($)
Plant A B C Capacity
P1 900 1125 875 25
P2 850 1200 950 25
Demand 20 11 18

Formulate and solve all-integer model that will determine how many tons of each type of coffee beans are produced in each plant by minimizing the total cost.

For this mathematical programming optimization problem:
Formulate and solve the model on Microsoft EXCEL Solver and prepare a Managerial Report that includes...

• A detailed introduction and explanation of the setting. Embellish if you wish!
• A complete formulation of the linear optimization model.
• Explain all variables, the objective, and constraints well.
• Provide the Microsoft EXCEL Solver output.
• Answer any questions posed in the problem.
• Provide and thoroughly interpret the reports from EXCEL Solver and note any interesting or more insightful output.

• After you have finished everything (described, formulated, solved, answered all questions, and written all of the report), create a one-page "Executive Summary" that indicates what the problem is, what you did to solve it, the final solution, and any other interesting results. This synopsis is for the busy executive who wants to see what is in the report and look at details further if interested.