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ds/ehab.pdf Instruction: Answer only FOUR (4) out of SIX (6) questions. Each que

ID: 3148746 • Letter: D

Question

ds/ehab.pdf Instruction: Answer only FOUR (4) out of SIX (6) questions. Each question is worth 20 points a) The selling price for each item of a product is RM50, and the total cost is given by C(x) 10x + 160, where x is the number of items. Write the profit function. Find the profit when x = 10 Find the number of units that gives the break-even point. Find the level of breakeven point if the total cost increases by 10%. (3 points) ii. (3 points) iii. (4 points) Suppose consumers will demand 30 units of a product when the price is RM12 per units and 20 units when the price is RM 18 each. Find the demand equations, assuming that it is linear. Find the price per unit when 10 units are demanded. b) (5 points) A company plans to phase out one model of its product and replace it with a new model. An advertising campaign for the product being replaced just ended, and typically after such a campaign, monthly sales volume S (in ringgit) decays according to c) S-22,000e 03S where t is in months. When the monthly sales volume for this product reaches RM 2500, the company plans to discontinue production and launch the new model. How long will it be until this happens? (5 points) QUESTION 2 a) For the revenue function given by R(x)-360x +8x-x find the maximum average revenue.

Explanation / Answer

(i) Given Selling price is RM 50=> S(x)= 50x

Cost C(x)= 10x+160

let profit function be P(x) = S(x)-C(x)

=50x-10x-160

therefore, P(x)=40x-160

for x=10

P(10)= 400-160= 240

therefore profit for =10 is RM240.

(ii) At breakeven the profit is 0

thus P(x)=0 => 40x-160=0

=> 40x=160

=> x=4

Therefore 4 items gives a breakeven.

(iii) If cost increase by 10% the new C'(x)=(1.10)*(C(x))

=( 1.10)(10x+160)

C'(x)=11x+176

P'(x)=50x-11x-176

P'(x)=39x-176

At breakeven P'(x)=0

39x-176=0

=> x=176/39= 4.513

therefore breakeven happens at 4.513 which is about 12.825% increase. It can be rounded off to 5.