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SPECIAL CASES 251

where
x 1 ¼ kilos of fuel additive produced
x 2 ¼ kilos of solvent base produced

10 Suppose a company manufactures three products from two raw materials. The amount of
raw material in each unit of each product is given.

Raw Material Product A Product B Product C

I 7 kilos 6 kilos 3 kilos
II 5 kilos 4 kilos 2 kilos

If the company has available 100 kilos of material I and 200 kilos of material II, and if the
profits for the three products are E20, E20 and E15, respectively, how much of each
product should be produced to maximize profits?
11 Liva’s Lumber manufactures three types of plywood. The following table summarizes the
production hours per unit in each of three production operations and other data for the
problem.

Operations (hours)

Plywood I II III Profit/Unit
Grade A 2 2 4 E40
Grade B 5 5 2 E30
Grade X 10 3 2 E20
Maximum time available 900 400 600

How many units of each grade of plywood should be produced?
12 Set up the tableau form for the following linear programme (do not attempt to solve):

Max 4x 1 þ 2x 2 3x 3 þ 5x 3
s:t:
2x 1 1x 2 þ 1x 3 þ 2x 4 50
3x 1 1x 3 þ 2x 4 80
1x 1 þ 1x 2 þ 1x 4 ¼ 60
x 1 ; x 2 ; x 3 ; x 4 0

13 Set up the tableau form for the following linear programme (do not attempt to solve):
Min 4x 1 þ 5x 2 þ 3x 3
s:t:
4x 1 þ 2x 3 20
1x 2 1x 3 8
1x 1 2x 2 ¼ 5
2x 1 þ 1x 2 þ 1x 3 12
x 1 ; x 2 ; x 3 0

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