(a)Humphrey received an inheritance of $15,000 which he divided into three parts and invested in the treasury bills: in 91-day billpaying 3% annual interest; in 182-day bill paying 4% annual interest; and in 364-day bill paying 7% annual interest. He invested $5,000 more in 182-day bill than in 364-day bill. Humphrey earned $700 in interest the first year. Use the matrix inverse method to determine how muchHumphrey invested in each type of bill. (Your matrix should be a three by three)(6 Marks)

(b) Maxxis industries specialized in selling car tyres, have a demand of 650 tyres per week. They sell these at Ksh30,000 per tyre.The marginal price demand function, p'(x), for x number of tyres per week, is given as

(i)Find the price-demand equation.(3 Marks)

(ii)If the industry sells 1000 tyres per week, what price should it set?(3 Marks)

(c)Wendy refers you to Messi co. where the marginal revenue function of the company is given by the expression while its average cost is given by the expression where q represents the number of units produced and sold by Messi company.The directors require you to advise them on;

(i)The total revenue, total cost and total profit functions.

(ii)The quantity which would maximize the profit and revenue.

(iii)Maximum profit and revenue that can be attained.