Question

Required information

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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			X-3
Price per unit	$	128		$	228		$	456
Variable cost per unit	$	64		$	132		$	268
Machine hours per unit		1.0			2.5			4.0
Maximum units demand per period		335,000			164,000			41,000

The single machine used for all three products has a maximum capacity of 638,000 hours per period.

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 363,000 hours (instead of 638,000 hours). What is the maximum Clarke would be willing to pay for an increase of twenty (20) machine hours?

d. At what capacity (in machine hours) would the machine no longer be a bottleneck?

Answer 1

Answer with working notes is given below

Price per unit Variable cost Contribution per unit Machine hours Contribution per machine hour Ranking X-1 $128.00 $64.000 $64.00 1.00 $64.00 X-2 $228.00 $132.00 $96.00 2.50 $38.40 X-3 $456.00 $268.00 $188.00 4.00 $47.00 1 X X-1 335,000 -2 164,000 X-3 41,000 Allocation of machine hours Maximum demand Total machine hours allocated (In order of ranking) X-1 (335,000*1) X-3 (41,000*4) Balance machine hours to X-2 Total machine hours 335,000 Machine hours 335,000 164,000 164,000 139,000 164,000 638,000 139,000 139,000 335,000 X-1 335,000 X-2 | 55,600 X-3 41,000 а Output produced X-2 produced = 139,000/ 2.5 b Maximum willing to pay for increase of 20 machine hours 768 (20 * $38.40) Explanation: Contribution per unit of X-2 is relevant since it is not produced due to machine hour constraint Maximum willing to pay for increase of 20 machine hours 940 (20 * $47) If maximum hours is 363,000 Machine hour allocation X-1 X-3 335,000 28,000 (balance) Contribution per unit of X-3 is relevant since it is not produced due to machine hour constraint At 909,000 machine hours machine would not longer be a bottleneck 1 Total Maximum demand Machine hours per unit Total machine hours X-1 335,000 1 335,000 X-2 164,000 2. 5 410,000 X-3 41,000 4 164,000 909,000