Example: Product processing

A little bit more complicated example similar to Example: Product planning which contain more explanations.

1. Text
A firm produces four products: A, B, C, and D. Each unit of product A requires two hours of milling, one hour of assembly, and \$10 costs. Each unit of product B requires one hour of milling, three hours of assembly, and \$5 costs. Each unit of C requires 11/2 hours of milling, 21/2 hours of assembly, and \$2 costs. Finally, each unit of product D requires five hours of milling, no assembly, and \$12 costs.

The firm has 120 thousand hours of milling time and 160 thousand hours of assembly time available. In addition, not more than \$1 million may be tied up in in-process inventory.

Each unit of product A returns a profit of \$40; each unit of 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 20,000 units of product A can be sold; not more than 16,000 units of

product C can be sold; and any number of units of products B and D may be sold. However, at least 10,000 units of product D must be produced and sold.

The objective of the firm is to maximise the profit resulting from the sale of the four products.

Note: Even if the text looks hopeless it helps a lot to organise it into tables.

2. Tables

 Milling (hours per unit) Assembly (hours per unit) Costs (\$ per unit) Product A 2 1 10 Product B 1 3 5 Product C 1.5 2.5 2 Product D 5 0 12 Total disposable 120 hours of milling 160 hours of assembly 1 000 000

Table 1: Production requirements

 Minimum sails (units) Maximum sails (units) Profit (\$ per unit) Product A Any number 20 000 40 Product B Any number Any number 24 Product C Any number 16 000 36 Product D 10 000 Any number 23

Table 2: Sales characteristic