Question

The Advanced Engineering Economic Company ('AEE') is currently making its product (MEM502) in a process-focused shop, where rental payments are $8000 per year and material costs are $40 per unit. Records show that AEE currently sells 200 units of the product MEM502 for $200 each. As the manager of AEE, you are considering a proposed repetitive focus in order to lowest costs, and hence, lower prices; thereby raising the demand. the proposed shop however, has rental payments of $24,000 per year and material costs of $10 per unit.

a) Formulate the total cost and profit function for AEE (show full solution)

b) if a price of $80 will allow 400 units to be sold, using the Analytical method, determine what profit(or loss) the proposed new process can generate. (show full solution)

C) determine the new break-even quantity and total cost using the graphical method.

d) as the manger of AEE, would you change the process? Explain why

Answer 1

	a)	Cost Function:
		Current Process
		TC=40Q+8000
		TC=Total Cost
		Q=Quantity Produced
		Sales Revenue =200Q
		Profit (P)=200Q-40Q-8000
		P =160Q-8000
		NEW PROCESS:
		TC=10Q+24000
		P=200Q-10Q-24000=190Q-24000
		b)
		If Sales Price is $80
		Profit Function:
		P=80Q-10Q-24000=70Q-24000
		Q=400
		P=70*400-24000=$4,000
		Profit =$4,000
		C)Graphical Method	Q	P=70Q-24000
			Quantity	Profit
			100	-$17,000
			200	-$10,000
			300	-$3,000
			343	$10
			400	$4,000
			500	$11,000
		D)Profit with existing Process for 200 units
		P=160*200-8000=	$24,000
		Profit for new process with Q=200:
		190*200-24000=	$14,000
		Profit for new process with Q=400	$4,000
		Profit will decrease
		Process should not be changed
						X axis: Quantity, Y-Axis: Profit (Breakeven point=343) $15,000 $10,000 $5,000 50 100 300 400 500 600 -$5,000 -$10,000 -$15,000 -$20,000