Question

Required information [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. Price per unit Variable cost per unit Machine hours per unit Maximum units demand per period X-1 $ 168 $ 84 1.0 385,000 X-2 268 142 2.5 184,000 X-3 $ 536 $ 308 4.0 71,000 The single machine used for all three products has a maximum capacity of 838,000 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 453,000 hours (instead of 838,000 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

Bottleneck resources are the limited resources available which will not allow production of all the products due to its limited availability, so the product with highest contribution margin per bottle neck resources should be produced first.

we will find contribution margin per machine hours

	X1	X2	X3
Sales	$168	$268	$536
Variable costs	($84)	($142)	($308)
Contribution margin (Sales-variable cost)	$84	$126	$228
Machine hour per unit	1	2.5	4
Contribution margin per hour	$84($84/1)	$50.4($126/2.5)	$57($228/4)
Ranking	1	3	2

we will first produce product X-1 than X3 and than X2

	X1	X3	X2
Maximum demand	385,000	71,000	184,000
Machine hour per unit	1	4	2.5
Total machine hour required for X1	385,000
Machine hour left after producing X1	453,000(838,000-385,000)
Total machine hour required for X3		284,000(71,000*4)
Machine hours left after producing X1 & X3		169,000(453,000-284,000)
Machine hours for X2			169,000
Units produced of X2			67,600(169,000 hours/2.5 hours per unit)

So, units to be produced

X1=385,000

X3=71,000

X2=67,600

2)With an increase in 20 machine hours clarke can produce X2. SO maximum that can be paid is contribution margin of X2. Any amount higher than contribution margin of X2 will result into loss.

SO maximum = 20 hours*$50.4 contribution margin per hour of X2

=$1,008

3)if the maximum capacity was 453,000it will be used for producing X1 (385,000 units ) & X 3 (453,000-385,000)/4=17,000 units. As an entire demand of X3 is not fulfilled any additional available hours will be used for production of X3

SO maximum that should be paid = Contribution margin per hour of X3*20hours

=$57*20

=$1,140

4)If the demand of all the units are fulfilled there will be no bottleneck

Total machine hours = (X1 maximum units*machine hours for producing one unit of X1)+(X2 maximum units*machine hours for producing one unit of X2)+(X3 maximum units*machine hours for producing one unit of X3)

(385,000*1)+(184,000*2.5)+(71,000*4)

=1,129,000 hours

Thus, At 1,129,000 machine hours capacity availability there will be no bottleneck