Question One

1. a)The switching patterns of customers visiting supermarkets P, Q and R are shown below:

TO

FROM. P. Q. R

P 5340. 1260. 1515

Q 1100. 4278. 1200

R 1097. 1178. 3567

i) Determine the transition matrix for this data.

ii) If a client is in supermarket Q in period 1, find the probability of being in supermarket R in period 3.

b) Ken Ltd. has estimated the revenue function R = 10 - 4q^2 and the cost function

C = q + 2. Determine the total net profit between the breakeven points.

c) The demand function P = 900 -3Q^2 and supply function P = Q^2 +500. Determine the producers' and consumers' surpluses.

Question Two

2. a) The average revenue AR = 1,000 - 10q^2 and the marginal cost MC = 16q + 90. When 20 units are sold the total cost is Sh. 6,000. Determine the maximum profit.

b) Solve the following simultaneous equations using the inverse matrix method.

4a + 3b - c = 26

5a - b + 2c = 58

3a + 2b + c = 24

c) Jack Ltd. has established its profit function as:

P = 6160x + 6600y - 44x^2 -33y^2 - 132xy.

i)Determine the maximum profit.

ii) Use the stationary conditions to show it's maximum profit.