Question

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	$	100		$	200		$	400
Variable cost per unit	$	50		$	120		$	240
Machine hours per unit		1.0			2.5			4.0
Maximum units demand per period		300,000			150,000			20,000

The single machine used for all three products has a maximum capacity of 500,000 hours per period.

Required:

a. A local engineering firm claims it can revise the production process such that product X-2 only requires 1.6 machine hours on the shared machine. How much would Clarke be willing to pay per period for the new process?

b. Suppose, instead, that the local engineering firm can revise the production process such that Product X-3 only requires 3.5 machine hours on the shared machine. (Product X-2 requires 2.5 machine hours as in Problem 4-75.) How much would Clarke be willing to pay per period for the new process?

Answer 1

		Amount in $
S.No	Particulars	X1	X2	X2
1	Price per unit	100	200	400
2	Variable cost per unit	50	120	240
3	Contribution per unit (1-2)	50	80	160
4	Rank	3	1	2
5	Machine hours per unit	1	2.5	4
6	Contribution per Machine hour (3/5)	50	32	40
7	Rank	1	3	2

Part a:

If the new process of local engineering is adopted :-

Machine hours required by product X2 is 1.6 hrs. Therefore, revised contribution per machine hour is:

		Amount in $
S.No	Particulars	X1	X2	X2
1	Price per unit	100	200	400
2	Variable cost per unit	50	120	240
3	Contribution per unit (1-2)	50	80	160
4	Rank	3	2	1
5	Machine hours per unit	1	1.6	4
6	Contribution per Machine hour (3/5)	50	50	40
7	Rank	1	1	2

In comparison to when X2 required 2.5 machine hours per unit. The additional contribution per machine hour is (50-32) $ 18 per machine hr.

Hence, clark would be willing to pay

Minimum : Variable cost for the period

120/1.6*500,000= $ 37,500,000

Maximum : Variable cost for the period + Excess contribution earned

120/1.6*500,000 + (18*500,000) $9,000,000 = $ 46,500,000

Part b:

If the new process is adopted, machine hours required by X3 would be 3.5 hrs. Therefore, revised contribution per machine hour will be-

		Amount in $
S.No	Particulars	X1	X2	X2
1	Price per unit	100	200	400
2	Variable cost per unit	50	120	240
3	Contribution per unit (1-2)	50	80	160
4	Rank	3	2	1
5	Machine hours per unit	1	2.5	3.5
6	Contribution per Machine hour (3/5)	50	32	46
7	Rank	1	3	2

Hence, clark would be willing to pay

Minimum : Variable cost for the period

240/3.5*500000= $ 34,285,714

Maximum : Variable cost for the period + Excess contribution earned

240/3.5*500000 + 6*500000 = $ 37,285,714