Question

A company is trying to maximize its profit on the sale of items A, B, and C. They make a profit of 60 dollars on each item of type A, 25 dollars on each item of type B, and $50 on each item of type C. Each product requires polishing and assembling time. Type A items requre 4 minutes of polishing, type B items require 3 minutes of polishing, and type C items require 5 minutes of polishing. Type A items use 2 minutes of assembly time, and types B and C items each use 1 minute of assembly time. There are 356 minutes of polishing time and 240 minutes of assembly time available. The company must produce at least 40 items of type A and 52 items of type B.

(a) The initial simplex tableau has:
  rows
  columns

(b) What is the maximum profit?
$  

This profit is obtained by making:
items of type a

items of type b

items of type C

Answer 1

(a)

5 rows

9 columns

(b)

4300

(c)

50 items of type A

52 items of type B

0 items of type C

Explanation:

Maximize Z = 60x1 + 25x2 + 50x3 subject to
4x1 + 3x2 + 5x3 <= 356
2x1 + x2 + x3 <= 240
x1 >= 40
x2 >= 52

Optimal Solution: z = 4300; x1 = 50, x2 = 52, x3 = 0