1. a)Mr. Rahim borrowed tk. 70000 from a bank and singed a promissory note bearing interest at 8% p.a compounded quarterly for 3 years and on the maturity date he paid the interest in full. Also he signed a second note without interest for the next 2 years. He borrowed Tk. 500000 with 10% interest rate.

I) Define EIR and determine the amount of interest paid in the 1st note.

ii) Find the face value of the 2nd note.

b)Mr. Kashem deposited Tk.2000 to a bank at an interest rate of 9% p.a. compounded quarterly when his son was 2 years 6 months and continued to deposit Tk. 2000 each six months until his son was 8 years old, when the last deposit was made. On his 10th birthday the son received the money in full.

i. How much money did the son receive on his 10th birthday?

ii. Prepare a sinking fund schedule for the deposits.

2. a) A revenue function of a company's product is defined by

f(x) = x-3x- 45x-30; where x stands for quantity of the product.

i. Test whether the function is increasing or decreasing; concave or convex at x= 4. Also find the critical points and point of inflection, if possible.

ii. Determine the number of units to maximize revenue and also calculate the maximum revenue.

b)What is Producer's surplus? Find the equilibrium price and quantity and then find the consumer's surplus and producers' surplus at the equilibrium price level if p=D(x)= x- 5 and p=S(x) =2x+30;where x stand for quantity.

3. a) The total profit function of a company is defined by

P(x, y) = 60x+34y-6x-4xy-3y+5; where x & y stands for two types of goods.

i. Define constraint optimization.

ii. Differentiate partially the function upto 2nd order and hence evaluate at (-3,4)

iii. If the company has a production quota x+y=10, determine how many units of each good should be produced and sold in order to maximize total profit and what is the maximum profit?

b) The marginal cost function is defined by MC= 3x2+2x-5; where x stands for quantity.

i. Determine the total cost function whose fixed cost is tk. 4000

ii. What is additional cost for producing 80 units to 120 units?