UNIVERSITY OF PROFESSIONAL STUDIES, ACCRA (UPSA)
BCPC 208: QUANTITATIVE METHODS (Take Home IA)
Date: 22nd April, 2020 Time Allowed: 48 Hours
INSTRUCTION: answer all questions on this question paper and pay attention to details
Question 1
Stonewall receives ยข250 per year in simple interest from an amount of money he invested in
ADB, Barclays and GCB. Suppose ADB pays an interest of 2%, Barclays pays an interest of
4% and GCB pays an interest of 5% per annum and an amount of ยข350 more was invested in
Barclays than the amount invested in ADB and GCB combined. Also, the amount invested in
Barclays is 2 times the amount invested in GCB.
a) Write down the three linear equations and represent them in the matrix form
๐ด๐ = ๐ต
.
b) Find the amount of money Stonewall invested in ADB, Barclays and GCB using Matrix
Inversion
Question 2
A manager hires labour and rents capital equipment in a very competitive market. Currently
the wage rate is GHยข2 per hour and capital is rented at GHยข5 per hour, the unit price of the
product is GHยข0.25 and total cost is 1000. Suppose the firmโs production function is as
follows:
๐& = &14๐พ*.,๐ฟ*., & + &10
i. What is the amount of labour and capital the firm should employ in order to maximize
output? [Hint: Maximise the product function subject to the cost constraint]
ii. What is the maximum profit?
Question 3
Miss Quaye is an entrepreneur is an entrepreneur who specializes in the production of wig
caps from Brazilian virgin hair. She purchase most of her virgin hair from the online trading
store Alibaba Express. In order to maximise profit in the short run, she employed an
economist to estimate the demand curve for her product, which was used to derive the
marginal revenue (MR) function for her product as:
๐๐
=24 โ 4๐
The economist also derived the marginal cost function (MC) for her product as:
๐๐ถ = 3๐6โ19๐ + 42
To be able to determine the amount of goods she has to produce in order to maximise profit,
she employed you at a cheaper cost than the economist, to:
a) Find the total revenue function and deduce the corresponding demand equation.
b) Find the total cost function if the fixed cost are ยข10.
c) Determine the number of wig caps that maximizes the Miss Quayeโs profit using first
and second order conditions.
d) How much should the Miss Quaye charge for one wig cap?
e) Find the total profit at the profit maximizing level of output.
