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