Question

QUESTION 1 [5 MARKS] A bank lent $200,500 for the development of two products. If the loan for product X was for $50,500 more than that for product Y, how much was lent for product Y? QUESTION 2 (10 MARKS] Solve for i in the following equation by means of linear interpolation (1 + i)0 - 1 = 25 QUESTION 3 (10 MARKS] A bakery finds that the price they can sell cakes is given by the function p 580 - 10x where x is the number of cakes sold per day, and p is price. The total cost function of the company is given by c = (30+5x) where x is previously defined, and c is total cost. A. Find the revenue and marginal revenue functions (Hint: revenue is price multiplied by quantity i.e. revenue = price X quantity] (3 marks) B. Find the fixed cost and marginal cost function (Hint: fixed cost does not change with quantity produced) (3 marks) C. Find the profit function (Hint: profit is revenue minus total cost] (2 marks) D. Find the quantity that maximizes profit (2 marks) QUESTION 4 (10 MARKS] A loan of $1400 is due in 1 year at a simple interest rate of 12%. Partial payments of $400 in 2 months, $25 in 6 months, and $700 in 8 months are made A. Construct a timeline clearly showing the timing of the debt and all repayments. (1 marks) B. Determine the balance due at the end of the 12 months using the merchant rule (6 marks) C. Determine the balance due at the end of the 8 months using the declining balance method (4 marks)

Answer 1

Let the Y be for amount of ea" then product X be money loaned for amount of money ea+50500 product loaned. for We know, development total money of two loaned products - at at 50500 = 200500 - 20 = 200 500 - 50500 7 20= 150000 - a= 75000) development of so money product loaned for ris $75000

3) P(x) = 580-10x C(X) = (3ot5x)² = A.) Revenue function, R(DL)= x (pal) = x (580-10x) - [RW) = 5801-1012 . Marginal Revenue function is s R(x)= 580-200 B) fixed cost fixed cost = Total cost col fixed cost = C(O) I fixed cost = $900

marginal cost function, - c'(x)=2(30+5%) x 5 c'al - 10 (30+ 5%

c) profil function is , S(0) S@= RO- c« - 580x - 10g ² - (250 +300x +90o) SOC) = 280X- 350- 900 o s'(x)=0 1 7 280-70x=0 1 [x = 40 d=40 maximizes proft.