UNIVERSITY OF EDUCATION, WINNEBA

MID SEMESTER TAKE HOMES EXAM

BBA 121: QUANTITATIVE TECHNIQUES

Instruction: Answer all questions. Your response to these questions MUST be

submitted through the UEW Learning management not later than 11.59pm 30th

May, 2020.

Assignment – Linear Programming

Question 1

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.

Required:

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.

Required:

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.

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