Question

QUESTION 4

1. Company ABC is a manufacturing company specialized in three auto parts denoted by X, Y, and Z respectively. The company is preparing for the budgets for the next year and has collected the following information:

	X	Y	Z
Raw materials costs /unit	$20	$30	$40
Labor hours needed /unit	0.3	0.2	0.1
Machine hours needed /unit	0.5	1	0.9
Market demand in units	10,000	20,000	15,000
Price in $	$55	$70	$85

1. The company allocates $10 of variable overhead cost to each labor hour.
2. The total fixed cost for the entire company is $300,000.
3. The company has a total labor budget of $50,000 with an hourly labor cost of $10.
4. After calculation, it costs $0.5 to run the machine for 1 hour. Company’s total budget for running machine is $20,000.

Required: (Please note that you should answer the questions in Word offline and please do NOT answer in the Blackboard!!!)

5. Does the company have any constraint? If yes, what is the constraint?
6. Given the constraint, what is the optimal production plan for the company that maximizes the company’s profit?
7. Company ABC has another two products: A and B. A can be sold “as is” (price: $300) or processed further into product A1 (price: $500). B can be sold “as is” (price: $200) or processed further into product B1 (price: $280). The allocated joint costs of A and B are $20 and $10, respectively. The cost of further processing costs of A and B are $185 and $78, respectively. Which product should be processed further and why?

Answer 1

1. Yes, there are following 2 constraint:-

a. first is Labor Hours, as company has budget of target labor cost of $50000 with an hourly labor cost of $10

so budget of labor hours = $50000/$10= 5000 Hours.

b. Second is Machine Hours, as Company’s total budget for running machine is $20,000 and  it costs $0.5 to run the machine for 1 hour, so total machine hours available i.e. bugdeted are $20000/$0.5= 40000 Hours.

2. Calculation of optimal production plan for comapny

Working note 1. calculation of Rank of products in terms of Contribution:-

Particular	X	Y	Z
Raw Material Cost/unit	$20	$30	$40
Labor cost/unit =labor hour needed*$10	0.3*$10= $3	0.2*$10= $2	0.1*$10= $1
Machine Cost/unit= Machine hour needed * $0.5	0.5*$0.5= $0.25	1*$0.5= $0.5	0.9*$0.5= $0.45
Variable Cost= Labor hour*$10	$3	$2	$1
Total Variable cost	$26.25	$34.5	$42.45
Price	$55	$70	$85
Contribution(Price- Total Variable cost)	$28.75	$35.5	$42.55
Rank	3	2	1

So From above Ranking first we produce Product Z then Product Y and then Product X.

Constraint are Labor hour(5000 Hour) and Machine hour(40000 Hour)

Calculation of Optimal production

Product/Constraint	Labor Hour	Machine Hour	Available
Z	15000*0.1= 1500 hours	15000*0.9= 13500 Hours	3500Hours of Labor and 17500 of Machine Hour
Y	17500*0.2= 3500 hours	17500*1 = 17500Hours	Zero hours of Labor and Machine
Total	5000 hours	40000 Hours

So Maximum Production with Given Constraint is 15000 units of Product Z and 17500units of Product Y.

3. Company ABC has another two products: A and B. A can be sold “as is” (price: $300) or processed further into product A1 (price: $500). B can be sold “as is” (price: $200) or processed further into product B1 (price: $280). The allocated joint costs of A and B are $20 and $10, respectively. The cost of further processing costs of A and B are $185 and $78, respectively.

So If product 'A' is Sold without further processing then profit is= $300-$20= $280

If product 'A' is further processed and product A1 is Sold then profit is= $500-$300-$185= $15

So If product 'B' is Sold without further processing then profit is= $200-$10= $190

If product 'B' is further processed and product B1 is Sold then profit is= $280-$200-$78= $2

So Product A should be further processed as Profit in further processing of product A is more than the Product B.