BBA 121: QUANTITATIVE TECHNIQUES
Instruction: Answer all questions.
Assignment – Linear Programming
Hopp Co (HC) manufactures and sells popular shoes and standard shoes. The Shoes,
both use the same type of good quality leather (bonner leather) which can be difficult
to source in sufficient quantity. The supply of bonner is restricted to 5,400 kg per
period and costs GHS40 per kg.
The shoes are made by skilled craftsmen (highly skilled labour) who are well known
for their workmanship. The skilled craftsmen take years to train and are difficult to
recruit. HC’s craftsmen are generally only able to work for 12,000 hours in a period.
The craftsmen are paid GHS18 per hour. HC sells the shoes to a large market.
Demand for the shoes is strong, and in any period, up to 15,000 popular shoes and
12,000 standard shoes could be sold. The selling price for popular shoe is GHS41 and
the selling price for standard shoe is GHS69. Manufacturing details for the two
products are as follows:
. Popular shoe Standard shoe
Craftsmen time per shoe 0·5 hours 0·75 hours
Bonner leather per shoe 270 g 270 g
Other variable costs per shoe GHS1·20 GHS4·70
HC does not keep inventory.
a) Calculate the profit earned from each shoe.
b) Identify the limiting factor(s)
c) Determine the optimal production plan for a typical period assuming that HC
is seeking to maximise the profit earned.
d) Calculate the maximum profit that could be earned
Some of the craftsmen have offered to work overtime, provided that they are paid
double time for the extra hours over the contracted 12,000 hours. HC has estimated
that up to 1,200 hours per period could be gained in this way.
e) Explain the meaning of a shadow price (dual price) and calculate the shadow
price of the limiting factor (s) identified in (b) above
f) Advise HC whether to accept the craftsmens’ initial offer of working overtime,
discussing the rate of pay requested, the quantity of hours and one other factor
that HC should consider.
Question 2 – Probability
A Health researcher is studying the prevalence of three health risk factors, denoted by
A, B, and C, within a population of women. For each of the three factors, the
probability is 0.1 that a woman in the population has only this risk factor (and no
others). For any two of the three factors, the probability is 0.12 that she has exactly
these two risk factors (but not the other). The probability that a woman has all three
risk factors, given that she has A and B, is 1/3.
Calculate the probability that a woman has none of the three risk factors, given that
she does not have risk factor A.