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i) Turning point is the point of local minima or maxima for a function. This point has zero slope.
ii) Second order derivative condition states that if the first derivative equals zero and the second
derivative is defined then the given point is a relative minimum if the second derivative is greater
than zero, or maximum if the second derivative is less than zero
iii) Partial derivative is the derivative of a multivariate function (function of more than one variable). It
is usually with respect to each of the independent variable.
iv) Mixed or cross partial derivative is obtained by first getting the derivative of multivariate function
with respect to one variable then the second derivative with respect to the second variable.
v) A saddle point is a stationery point that is neither a maximum nor a minimum. Here the difference
between the product of pure second partial derivative (second derivative of a function with respect
to one variable) and square of mixed partial derivative is less than zero
Mutiso answered the question on December 6, 2018 at 07:36
- On the study of costs and revenue for production of biro pens by a small company ACO Ltd, the
following expressions were determined. Before production starts...(Solved)
On the study of costs and revenue for production of biro pens by a small company ACO Ltd, the
following expressions were determined. Before production starts a set-up cost of Sh.1500 existed.
AR = 600 – 0.5q Average revenue
MC = 140 – 8q + 0.15q2 Marginal cost
Required:
i) The expression for profit.
ii) At what quantity q is profit maximized.
iii) Is this quantity q also the point that revenue is maximized?
Date posted: December 6, 2018. Answers (1)
- Two firms A and B in Nairobi Industrial area make glue. The cost functions for making glue for the twofirms are as follows:Firm A -...(Solved)
Two firms A and B in Nairobi Industrial area make glue. The cost functions for making glue for the two
firms are as follows:
Firm A - C = 0.2x + 200
Firm B - C = 0.6x + 50
Where x – is litres of glue produced in „000?.
Required:
By drawing a graph of these functions, show whose firm?s costs increase more rapidly.
Date posted: December 6, 2018. Answers (1)
- A company employs four classes of machine operators (A,B,C,D): all new employees are hired as class D
and, through a system of promotion, may work up...(Solved)
A company employs four classes of machine operators (A,B,C,D): all new employees are hired as class D
and, through a system of promotion, may work up to a higher class. Currently, there are 200 class D, 150
class C, 90 class B and 60 class A employees. The company has signed an agreement with the union
specifying that 20 percent of all employees in each class be promoted, one class in each year. Statistics show that each year 25 percent of the class D employees are separated from the company by reason such as retirement, resignation and death. Similarly 15 percent of class C, 10 percent of class B and 5 percent of class A employees are also separated. For each employee lost, the company hires a new class D employee.
Required:
i) The transition matrix.
ii) The number of employees in each class two years after the agreement with the union.
iii) The equilibrium state in number of employees.
Date posted: December 6, 2018. Answers (1)
- Define the following terms as used in Markovian analysis:
i) Transition matrix.
ii) Initial Probability vector
iii) Equilibrium
iv) Absorbing state(Solved)
Define the following terms as used in Markovian analysis:
i) Transition matrix.
ii) Initial Probability vector
iii) Equilibrium
iv) Absorbing state
Date posted: December 6, 2018. Answers (1)
- An electronics firm carries out a small-scale test launch of a new low-priced pocket calculator. It estimates from this test that if it went into...(Solved)
An electronics firm carries out a small-scale test launch of a new low-priced pocket calculator. It estimates from this test that if it went into full-scale production it would sell between 1,000 and 2,500 calculators per month, and that its monthly revenue in thousands of shillings over this range of sales could be represented by the equation:
R = - x2 + 5x
Where: x is the monthly output in thousands of calculators (it is assumed that it sells its entire output).
From experience of calculator production, the firm estimates its marginal cost in thousands of shillings
could be represented by the equation:
MC = x2– x + 2
and that its fixed costs will be Sh.500 per month.
Required:
i) Determine the average cost and revenue equations for this firm.
ii) Determine the profit-maximizing output, the price that should be charged to maximize profit, and how
much each calculator will then cost to make.
Date posted: December 6, 2018. Answers (1)
- The number of shoppers queuing at any given time in a certain supermarket in downtown Nairobi can be
approximately represented by the equation:(Solved)
The number of shoppers queuing at any given time in a certain supermarket in downtown Nairobi can be
approximately represented by the equation:
Required:
i) The management wants to know when they should deploy more cashiers and the number queuing at
that time.
ii) Determine the number of man-hours spent per day by shoppers queuing.
Date posted: December 6, 2018. Answers (1)
- XYZ Company Limited invests in a particular project and it has been estimated that after X months of
running,(Solved)
XYZ Company Limited invests in a particular project and it has been estimated that after X months of
running, the cumulative profit (Sh.„000‟) from the project is given by the function 10x-x2-5,
where x represents time in months. The project can run for eleven months at most.
Required:
i) Determine the initial cost of the project.
ii) Calculate the break-even time in months for the project.
iii) Determine the best time to end the project.
iv) Determine the total profit within the break-even points
Date posted: December 6, 2018. Answers (1)
- Gatheru and Kabiru Certified Public Accountants have recently started to give business advise to their
clients. Acting as consultants, they have estimated the demand curve of...(Solved)
Gatheru and Kabiru Certified Public Accountants have recently started to give business advise to their
clients. Acting as consultants, they have estimated the demand curve of a clients firm to be;
AR=200-8Q
Where AR is average revenue in millions of shillings and Q is the output in units.
Investigation of the client firm‟s cost profile shows that marginal cost (MC) is given by:
MC=Q2-28Q+211(In million shillings)
Further investigations have shown that the firm‟s cost when not producing output is sh.10 million.
Required:
i) The equation of total cost
ii) The equation of total revenue
iii) An expression for profit.
iv) The level of output that maximizes profit
v) The equation of marginal revenue.
Date posted: December 6, 2018. Answers (1)
- Two CPA students were discussing the relationship between average cost and total cost. One student said
that since average cost is obtained by dividing the cost...(Solved)
Two CPA students were discussing the relationship between average cost and total cost. One student said
that since average cost is obtained by dividing the cost function by the number of units Q, it follows that the derivative of the average cost is the same as marginal cost, since the derivative of Q is 1.
Required:
Comment on this analysis.
Date posted: December 6, 2018. Answers (1)
- Demand function for a firm is given by
P=12 - 0.4Q
P is the price of the product, Q is the quantity demanded, and the total cost...(Solved)
Demand function for a firm is given by
P=12 - 0.4Q
P is the price of the product, Q is the quantity demanded, and the total cost (C) is given by
C = 5 + 4Q + 0.6Q2
At what price and quantity will the firm have maximum profit? If the firm aims at maximizing sales, what
price should it charge?
Date posted: December 6, 2018. Answers (1)
- A company is selling an item for ps= Sh.5. Profit is related to selling price p by
P=50000ps - 6250ps
2
i ) Is the profit an increasing...(Solved)
A company is selling an item for ps= Sh.5. Profit is related to selling price p by
P=50000ps - 6250ps
2
i ) Is the profit an increasing function or a decreasing function when ps = 5?
ii) If the price is changed to Sh.4.75, find whether profit would increase or decrease and find the change in
profit.
iii) At what price is the profit maximized?
Date posted: December 6, 2018. Answers (1)