Question

Question 1:   The marketing department for your electronics company has determined the relationship between price and demand for a new smartphone: Price ($) = 150 – 0.01 x (Monthly Demand) The fixed costs for this item are $50,000 per month, and the variable cost per unit is $40.   Determine: a) What is the optimal production volume per month for this product? b) What is the maximum profit per month? c) What is the domain of profitable demand? d) Prepare a spreadsheet and chart that shows cost, revenue, and profit. (Use the chart type scatter with smooth lines, over a range of demand from 0 to 12,000 units per month. The chart must include axis titles and a legend that identifies the three curves.

Question 2: You hope to sell a product for $575 that has a variable cost per unit of $335.  Your fixed cost is from rent on the fully‐furnished factory in which your product is manufactured. a) If you sell 9000 units per year, what is the maximum monthly rent you can afford to pay in order to break even? b) If the rent was actually $58,000 per month, then what is your annual profit if you sell 7000 units per year?

Question 3: A regional airline is considering the addition of winglets to its CRJ200 aircraft, at a cost of $375,000 per plane. The winglets improve fuel economy from 3150 lbs of fuel per hour to 3020 lbs/hr. Assuming a fuel cost of $0.27 per lb, and an interest rate of 1% per month, how many hours each month must be flown in order for this upgrade to break even within 3 years?

Question 4: Your company has been renting forklifts at a cost of $7500 (each) per year.  If your company upgrades the warehouse to an integrated robotic system, then forklifts would no longer be needed. The upgraded warehouse costs $208,000 to construct, $11,000 each year to maintain, and will have a useful life of 25 years.  For an interest rate of 5% per year, how many forklifts could be rented each year and break even with the cost of the upgraded warehouse?  

Question 5: You have invested $26,500 to obtain equipment that enables you to generate $4550 in revenue each month, with monthly costs of $1725. For a monthly interest rate of 3%, how many months are required for you to pay off your initial investment?

Question 6: Your company has purchased surveying equipment for $43,500, and will utilize it for 8 years before selling it for $3250.  How much new revenue must this equipment generate each year in order to pay off the equipment and realize a return of 6% per year?  Note: solve this problem with the factor method or equation method, and then also set up a spreadsheet illustration of ‘Unrecovered Investment Balance’.  (Hint: we’ve done spreadsheets like this before, on HW 7 and ICE 12).

Answer 1

Question 1

Optimal Production will be at that level when Profit is equal to total cost. After that level profit will keep on reducing with falling prices i.e 5500 Units

Parameters	$
Price	150
Variable Price	150-0.01*(Monthly Demand)
Fixed cost	50000
Variable Cost	40
Price	150

(a)	(a)/1000	(b)= 150-0.01*(a)	('c)=(a)*(b)	d= (a)*40	e= ('c)-(d)	(f)	(g)=d+(f)	h=e-(f)
Monthly Demand	Units( in '000)	Sales Price	Revenue	Variable	Contribution	Fixed cost	Total Cost	Profit
0	0	150.00	0	0	0	50000	50000	-50,000
1000	1	140.00	140000	40000	100000	50000	90000	50,000
2000	2	130.00	260000	80000	180000	50000	130000	1,30,000
3000	3	120.00	360000	120000	240000	50000	170000	1,90,000
4000	4	110.00	440000	160000	280000	50000	210000	2,30,000
5000	5	100.00	500000	200000	300000	50000	250000	2,50,000
6000	6	90.00	540000	240000	300000	50000	290000	2,50,000
7000	7	80.00	560000	280000	280000	50000	330000	2,30,000
8000	8	70.00	560000	320000	240000	50000	370000	1,90,000
9000	9	60.00	540000	360000	180000	50000	410000	1,30,000
10000	10	50.00	500000	400000	100000	50000	450000	50,000
11000	11	40.00	440000	440000	0	50000	490000	-50,000
12000	12	30.00	360000	480000	-120000	50000	530000	-1,70,000

(a)	(a)/1000	(b)= 150-0.01*(a)	('c)=(a)*(b)	d= (a)*40	e= ('c)-(d)	(f)	(g)=d+(f)	h=e-(f)
Monthly Demand	Units( in '000)	Sales Price	Revenue	Variable	Contribution	Fixed cost	Total Cost	Profit
5000	5.00	100.00	500000	200000	300000	50000	250000	2,50,000
5100	5.10	99.00	504900	204000	300900	50000	254000	2,50,900
5200	5.20	98.00	509600	208000	301600	50000	258000	2,51,600
5300	5.30	97.00	514100	212000	302100	50000	262000	2,52,100
5400	5.40	96.00	518400	216000	302400	50000	266000	2,52,400
5500	5.50	95.00	522500	220000	302500	50000	270000	2,52,500
5600	5.60	94.00	526400	224000	302400	50000	274000	2,52,400
5700	5.70	93.00	530100	228000	302100	50000	278000	2,52,100
5800	5.80	92.00	533600	232000	301600	50000	282000	2,51,600
5900	5.90	91.00	536900	236000	300900	50000	286000	2,50,900
6000	6.00	90.00	540000	240000	300000	50000	290000	2,50,000