Question

! Required information Problem 4-75 and 4-76 (Static) (LO 4-4,5) [The following information applies to the questions displayed below) Clarke Corporation manufactures three products (X-1, X-2, and X-3) utilizing in one of the processes, a single machine for all products. Data on the individual products follow. X-1 X-2 Price per unit X-3 $ 100 $ 200 Variable cost per unit $ 400 50 $ 120 $ 240 Machine hours per unit 1.0 4.0 Maximum units demand per period 300,000 150,000 20,000 $ 2.5 The single machine used for all three products has a maximum capacity of 500,000 hours per period. Problem 4-75 (Static) Theory of Constraints (LO 4.4,5) Required: a. How many units of each product should be produced each period? b. A local engineering firm has suggested to Clarke that it might be able to increase the capacity on the machine. What is the maximum Clarke would be willing to pay for an increase of twenty (20) machine hours? c. Suppose the maximum capacity on the machine was 300,000 hours (instead of 500,000 hours). What is the maximum Clarke would

Answer 1

a.						X-1	X-2	X-3
	Price per unit					100	200	400
	Less:Variable cost per unit					50	120	240
	Contribution margin per unit				a	50	80	160
	Machine hours per unit				b	1	2.5	4
	Contribution margin per machine hour				a/b	50	32	40
	Rank					1	3	2

	First Preference should be given to X-1
	Total hours available=500000 hours
	Demand for X-1=300000 units
	Machine hours per unit=1
	Machine hours used for X-1=300000*1=300000 hours
	Balance machine hours available=500000-300000=200000
	Second Preference should be given to X-3
	Demand for X-3=20000 units
	Machine hours per unit=4
	Machine hours used for X-3=20000*4=80000 hours
	Balance machine hours available=200000-80000=120000
	last Preference should be given to X-2
	Machine hours per unit=2.5
	Units of X-2 can be produced=120000/2.5=48000
	X-1	300000	units
	X-2	48000	units
	X-3	20000	units
b.	Maximum amount payable=20*Contribution margin per hour for product with unfulfilled demand (X-2)=20*32=$ 640
c.	First Preference should be given to X-1
	Total hours available=300000 hours
	Demand for X-1=300000 units
	Machine hours per unit=1
	Machine hours used for X-1=300000*1=300000 hours
	Balance machine hours available=300000-300000=0
	Second Preference should be given to X-3
	Maximum amount payable=20*Contribution margin per hour for product with unfulfilled demand (X-3)=20*40=$ 800
d.	Capacity that is no longer a bottleneck=Machine hour which fulfills the demand of all products
	Capacity:
		Demand	Machine hours per unit	Total machine hours
		a	b	a*b
	X-1	300000	1	300000
	X-2	150000	2.5	375000
	X-3	20000	4	80000
	Total			755000
	Capacity=755000 machine hours