a) Discuss the areas of application of business mathematics to a manager (5 marks)
b) Highlight four assumptions of markov process (4 marks)
c) If A={m,n,o,p} B={m,o,p,q} C={m,p,r} and the universal set is defined as U={k,l,m,n,o,p,q,r,s,t} then what is:
i)AUB ii) AUC iii) BnC iv) (AUB)’ v) (AnC)’ (4 marks)
d) Given the following demand function; Q=(40- 2P)/3 ; where Q is the level of output and P, the price per unit. The cost function is defined as TC= 0.5Q2 + 10Q-225.
i. Derive the revenue function and the cost function.
ii. Calculate the corresponding break-even point. (6 marks)
e) A firm has an advertising budget of shs 720 000. It wishes to allocate this budget to two media: magazines and televisions, so that total exposure is maximized. Each page of magazine advertisement is estimated to result in 60 000 exposures, whereas each spot in television is estimated to result 120 000 exposures. Each page of magazine advertisement costs shs 9000 and each spot in television advertising costs shs 12 000. Formulate the linear programming problem (6 marks)
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