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192 CHAPTER 4 LINEAR PROGRAMMING APPLICATIONS

c. Suppose that ten, six and eight hours of overtime may be scheduled in departments
A, B and C, respectively. The cost per hour of overtime is E18 in department A,
E22.50 in department B and E12 in department C. Formulate a linear programming
model that can be used to determine the optimal production quantities if overtime is
made available. What are the optimal production quantities, and what is the revised
total contribution to profit? How much overtime do you recommend using in each
department? What is the increase in the total contribution to profit if overtime is
used?

3 Hilltop Coffee manufactures a coffee product by blending three types of coffee beans. The
cost per kilo and the available kilos of each bean are as follows:

Bean Cost per kilo Available kilos
1 E0.50 500
2 E0.70 600
3 E0.45 400

Consumer tests with coffee products were used to provide ratings on a scale of 0–100, with
higher ratings indicating higher quality. Product quality standards for the blended coffee
require a consumer rating for aroma to be at least 75 and a consumer rating for taste to be at
least 80. The individual ratings of the aroma and taste for coffee made from 100 per cent of
each bean are as follows.

Bean Aroma Rating Taste Rating
1 75 86
2 85 88
3 60 75

Assume that the aroma and taste attributes of the coffee blend will be a weighted average of the
attributes of the beans used in the blend.
a. What is the minimum-cost blend that will meet the quality standards and provide 1000
kilos of the blended coffee product?
b. What is the cost per kilo for the coffee blend?
c. Determine the aroma and taste ratings for the coffee blend.
d. If additional coffee were to be produced, what would be the expected cost per kilo?
4 Ajax Fuels is developing a new additive for aeroplane fuels. The additive is a mixture
of three ingredients: A, B and C. For proper performance, the total amount of
additive (amount of A + amount of B + amount of C) must be at least ten grams
per litre of fuel. However, because of safety reasons, the amount of additive must
not exceed 15 grams per litre of fuel. The mix or blend of the three ingredients is
critical. At least one gram of ingredient A must be used for every gram of ingredient B.
The amount of ingredient C must be at least one-half the amount of ingredient A. If
the costs per gram for ingredients A, B and C are E0.10, E0.03 and E0.09,
respectively, find the minimum-cost mixture of A, B and C for each litre of
aeroplane fuel.

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