MANG1007W1
SEMESTER 1 EXAMINATIONS 2019-20
MANAGEMENT ANALYSIS
SECTION A
You must answer ALL TEN questions from this section.
A1.
a) What is the value of log28?
b) What is the value of e5 e3? [4 marks]
A2. John and Mary together have combined savings of £12,000. If John has £2,000 less than Mary, how much does each one of them have? [4 marks]
A3.
a) Can the equation y = 10 - 5x be represented as a line?
b) Is the value of the slope of this line 10, 5, or -5? [4 marks]
A4.
a) If an amount of £100 is put in a bank earning 5% compound interest a year, how much will it have become at the end of 10 years?
b) How many years will it take for the amount to surpass £110? [4 marks]
A5. Assume you have collected the observations 13, 16, 16, 21, 22, 24, and 30. What is the mean, median, and mode? [3 marks]
A6.
a) Ten friends are at a bar drinking. If all possible pairs that can be formed shake hands, how many handshakes are there?
b) If the ten friends decide to exchange coats, how many different allocations of coats to people are there? [4 marks]
A7. You throw a pair of dice three times. What is the probability that the sum of the two dice equals 12 on at least one of the three throws? Show your working. [5 marks]
A8. Which of the following statements are correct?
a) Regression is a method for solving linear programming problems.
b) Regression is often used in analytics.
c) Regression is technique of statistics. [4 marks]
A9.
a) Find the value of x that optimizes the function -5x2 + 40x + 500.
b) Does this value achieve a maximum or a minimum for the function? [4 marks]
A10. X is a normally distributed variable with mean 0. What is the probability that X is smaller than 0? [4 marks]
SECTION B
You must answer TWO questions from this section.
B1. A pub orders cartons of crisps as soon as it runs out. Assume that orders are delivered instantaneously. Each time the shop makes an order it pays a fixed cost £100. Demand is constant at D = 100 cartons per time unit. Storing the cartons in inventory incurs opportunity costs at a rate of 5% per £, time unit, and carton. Each carton’s value is £20.
a) How many cartons should the pub be ordering every time it places an order, in order to minimise cost per time (while
always meeting demand)? [20 marks]
b) Is the assumption of instantaneous delivery necessary for your answer to (a) to be correct? [10 marks]
B2. A plant makes two kinds of products, A and B. Each product
requires machine work and manual work. Each unit of A requires 1 hour of machine work and 2 hours of manual work. Each unit of B requires 2 hours of machine work and 2 hours of manual work. Each day, the plant has available 10 hours of machine work and 12 hours of manual work. Finally, each unit of A generates a profit of £4 and each unit of B generates a profit of £5.
a) Formulate this problem as a linear program. [10 marks]
b) What is the maximum profit the plant can achieve and how many units of A and B should it make in order to do so? [20 marks]
B3. A doctor’s surgery manager is concerned about the doctor’s
time being wasted by missed appointments. She is considering booking more patients into clinic times to ensure that the doctor will be busy even when some patients don’t show for appointments.
A morning clinic has time for 6 patients to be seen and on average 2 patients miss their appointments. The probability that a patient makes their appointment is 4/6. To address this, the manager is planning to book 8 patients for each morning clinic.
(a) Which probability distribution is most appropriate for modelling this situation? Explain your answer. [10 marks]
(b) Based on your answer to (a), calculate the probability that more than 6 patients arrive, and the doctor must either turn patients away or shorten their lunch break. [15 marks]
(c) If we were considering a larger group of patients and the probability of missing an appointment was very small. What other distribution might you consider to be appropriate for modelling the number of missed appointments? [5 marks]