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74 CHAPTER 2 AN INTRODUCTION TO LINEAR PROGRAMMING

13 GulfGolf also make two different types of golfing gloves: a regular model and a
professional model. The firm has 900 hours of production time available in its cutting and
sewing department, 300 hours available in its finishing department and 100 hours
available in its packaging and shipping department. The production time requirements and
the profit contribution per glove are given in the following table.

Production Time (hours)
Cutting and Packaging and Profit/
Model Sewing Finishing Shipping Glove

Regular model 1 0.5 0.125 $5
Professional’s 1.5 0.3333 0.25 $8
model

Assuming that the company is interested in maximizing the total profit contribution, answer
the following:
a. What is the linear programming model for this problem?
b. How many gloves of each model should GulfGolf manufacture?
c. What is the total profit contribution the company can earn with the listed production
quantities?
d. How many hours of production time will be scheduled in each department?
e. What is the slack time in each department?

14 A local health clinic is keen to raise awareness and understanding of AIDS/HIV in the local
community and has managed to attract some funding for local advertising. The clinic would like
to determine the best way to allocate a monthly advertising budget of E1000 between
newspaper advertising and radio advertising. Management has decided that at least 25 per cent
of the budget must be spent on each type of media, and that the amount of money spent on
local newspaper advertising must be at least twice the amount spent on radio advertising. A
marketing consultant has developed an index that measures audience exposure per euro of
advertising on a scale from 0 to 100, with higher values implying greater audience exposure. If
the value of the index for local newspaper advertising is 50 and the value of the index for spot
radio advertising is 80, how should the clinic allocate its advertising budget in order to maximize
the value of total audience exposure?
a. Formulate a linear programming model that can be used to determine how the clinic
should allocate its advertising budget in order to maximize the value of total audience
exposure.
b. Find the optimal solution using the graphical solution procedure.
15 Miguel’s Mexican produces various Mexican food products and sells them to Western
Foods, a chain of grocery stores located in Europe. Miguel’s makes two salsa
products: Western Foods Salsa and Mexico City Salsa. Essentially, the two products
have different blends of whole tomatoes, tomato sauce and tomato paste. The Western
Foods Salsa is a blend of 50 per cent whole tomatoes, 30 per cent tomato sauce and
20 per cent tomato paste. The Mexico City Salsa, which has a thicker and chunkier
consistency, consists of 70 per cent whole tomatoes, 10 per cent tomato sauce and 20
per cent tomato paste. Each jar of salsa produced weighs 280gms. For the current
production period Miguel’s can purchase up to 280 kilos of whole tomatoes, 130 kilos
of tomato sauce and 100 kilos of tomato paste; the price per kilo for these ingredients
is E0.96, E0.64 and E0.56, respectively. The cost of the spices and the other
ingredients is approximately E0.10 per jar. Miguel’s buys empty glass jars for E0.02

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