Question

Firm Z manufactures 3 products using the same machine. At the weekly market demand for the product (see below), the firm is limited in terms of machine capacity - 450 hours per week.

Product Machine hours required per unit of product Maximum demand in units Contribution margin per unit

A 3 hours machinery hours, maximum demand in units 100, Contribution margin £9

B 2 hours machinery hours, maximum demand in units 100, contribution margin £7

C 1 hour machinery hours, maximum demand in units 100, contribution margin £5

Required:

a) How many units of each product should the firm produce?

b) How much is the contribution (money) of each product in terms of machine hours used?

c) If the machine hours were limited to 300 hours, which product would you recommend to cease from the production process?

Answer 1

a) Units of each product produced by company

1st we have to calculate per hour contribution of each product

Particulars	Product A	Product B	Product C
Conrtibution per unit(A)	£9	£7	£5
No of hours required per unit(B)	3 hrs	2 hrs	1 hr
Per Hour Contibution(A/B)	£3	£3.5	£5

Total number of Machine Hopurs =450hrs

Maxmimum demand for each product =100 units

Hours required for max demend for each product are as follows:

Product A=100*3hrs=300hrs & per hours Contribution for Product A = £3

Product B=100*2hrs=200hrs & per hours Contribution for Product B = £3.5

Product C=100*1 hr=100hrs & per hours Contribution for Product C = £5

On the basis of highest contrbution per,1st produce Product A, next Product B & Product B as follows :

Particulars	Hours	Number of Units	Contribution per unit	Total Contribution
Total Hours	450
Used for Product C	100	100	£5	£500
Balance after production of Product C	350
Used for Product B	200	100	£7	£700
Balance after production of Product B	150
Used for Product A	150	50	£9	£450
Balance after production of Product A	0
Total Contribution	£1650

100 units of Product C,100 units of Product B & 50 units of Product A should firm produce

b) The contribution (money) of each product in terms of machine hours used

Particulars	Product A	Product B	Product C
Conrtibution per unit(A)	£9	£7	£5
No of hours required per unit(B)	3 hrs	2 hrs	1 hr
Per Hour Contibution(A/B)	£3	£3.5	£5

Particulars	Hours	Number of Units	Contribution per unit	Total Contribution	Per Machine Hour Contribution
Total Hours	450
Product A	150	50	£9	£450	£3
Product B	200	100	£7	£700	£3.5
Product C	100	100	£5	£500	£5
Total Contribution	£1550

c) If the machine hours were limited to 300 hours:

Product A should cease to be produce if machinbe hours are 300 beacuse Product A gives very low per hour contribution compared to Product A & Product B

for 300 hrs : Production & contribution are as follows :

Particulars	Hours	Number of Units	Contribution per unit	Total Contribution	Per Machine Hour Contribution
Total Hours	300
Product B	200	100	£7	£700	£3.5
Product C	100	100	£5	£500	£5
Total Contribution	£1200