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GENERAL LINEAR PROGRAMMING NOTATION 73

a. Show the feasible region.
b. What are the extreme points of the feasible region?
c. Find the optimal solution using the graphical procedure.
10 Refer to the GulfGolf problem described in Section 2.1. Suppose that management
encounters each of the following situations:
a. The accounting department revises its estimate of the profit contribution for the deluxe
bag to $18 per bag.
b. A new low-cost material is available for the standard bag, and the profit contribution per
standard bag can be increased to $20 per bag. (Assume the profit contribution of the
deluxe bag is the original $9 value.)
c. New sewing equipment is available that would increase the sewing operation capacity
to 750 hours. (Assume 10S +9D is the appropriate objective function.)
If each of these conditions is encountered separately, what are the optimal solution and the
total profit contribution for each situation?

11 Write the following linear programme in standard form:
Max 5x 1 þ 2x 2 þ 8x 3
s:t:
1
1x 1 þ 2x 2 þ / 2 x 3 420
2x 1 þ 3x 2 1x 3 610
6x 1 1x 2 þ 3x 3 125
x 1 ; x 2 ; x 3 0

12 RMC, Inc., is a small firm that produces a variety of chemical products. In a particular
production process, three raw materials are blended (mixed together) to produce
two products: a fuel additive and a solvent base. Each kilo of fuel additive is a mixture of 0.4
kilos of material 1 and 0.6 kilos of material 3. A kilo of solvent base is a mixture of 0.5 kilos
of material 1, 0.2 kilos of material 2 and 0.3 kilos of material 3. After deducting relevant
costs, the profit contribution is E40 for every kilo of fuel additive produced and E30 for
every kilo of solvent base produced.
RMC’s production is constrained by a limited availability of the three raw materials. For
the current production period, RMC has available the following quantities of each raw
material:

Raw Material Amount Available for Production

Material 1 20 kilos
Material 2 5 kilos
Material 3 21 kilos

Assuming that RMC is interested in maximizing the total profit contribution, answer the
following:
a. What is the linear programming model for this problem?
b. Find the optimal solution using the graphical solution procedure. How many kilos of
each product should be produced, and what is the projected total profit contribution?
c. Is there any unused material? If so, how much?
d. Are there any redundant constraints? If so, which ones?

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