# This problem sets up a linear programming problem.

A firm produces four products: A, B, C, and D. Each unit of product A requires 2 hours of milling, 1 hour of assembly and $10 worth of in-process inventory. Each unit of product B requires 1 hour of milling, 3 hours of assembly and $5 worth of in-process inventory. Each unit of product C requires 2.5 hours of milling, 2.5 hours of assembly and $2 worth of in-process inventory. Each unit of product D requires 5 hours of milling, no assembly (0 hours) and $12 worth of in-process inventory.

The firm has 120 hours of milling time and 160 hours of assembly time available. In addition, due to financial constraints not more than $1,000 may be tied up in in-process inventory.

Each unit of product A returns a profit of $40; each unit of product B returns a profit of $24; each unit of product C returns a profit of $36; and each unit of product D returns a profit of $23.

Not more than 20 units of product A can be sold; not more than 16 units of product C can be sold; and any number of units of product B and D may be sold. However, due to a contract requirement at least 10 units of product D must be produced and sold.

Assume that units are produced and sold in the same period.

Formulate the above as a linear programming problem to maximize the profit resulting from the sale of the four products.

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#### Solution Preview

Let:

X1 = Number of units of product A produced and sold

X2 = Number of units of product B produced and sold

X3 = Number of units of product C produced and sold

X4 = Number of units of product D produced and sold

Maximize P = 40 * X1 ...

#### Solution Summary

The solution sets up a linear programming problem to optimize the profit resulting from the sale of four products.