Question

A company manufactures 2 core trade items, A and B. Both products need manufacturing time in 3 stages which is shown below:

Stage	Capacity of stage	Item A	Item B
Cutting	100	8	1
Coating	50	1	1
Assembling	100	1	4
	TOTAL HOURS PER ITEM:	10	6

The chief plant officer (CPO) says that product A has a profit contribution (Price sold minus Variable Cost) of 20000 USD and product B of 16000 USD. The production capability is defined by the capacity of each stage. Questions: 1. If somebody could produce only product A, which could be the official contribution in the profits? 2. If the added time was used for production of product B, which could the total profit be? 3. Could you suggest to the CPO another production mix in order to achieve higher total profit and if yes which would be the percentage for each stage?

Answer 1

MAXIMUM NUMBER OF PRODUCTS THAT CAN BE PRODUCED (PART 1)

PARTICULARS	ITEM A (In Units No.)	ITEM B (In Units No.)
CUTTING	(100/8)=12.5	(100/1)=100
COATING	(50/1)=50	(50/1)=50
ASSEMBLING	(100/1)=100	(100/4)=25

All the three process are required for manufacturing Item A or Item B.As a result of which

Max. No.s of Item A that can be produced with the given capacity hours at the each stage is 12 Units.(As Part cannot be produced so rounding off 12.5 to 12)

Max. No of Item B is 25 Units.

If only product A is produced the total profit contribution would be USD 2,40,000           (12 Unit*20000 USD profit contribution per unit)

Added time at each stage after producing 12 Units of ITEM A

	Item A	Total Capacity	Excess Hours capacity
Cutting	12 Units*8 Hours Per unit of item A= 96 Hours	100	4 Hours
Coating	12 Unit * 1 hour Per Unit of Item A= 12 Hours	50	38 Hours
Assembling	12 Unit * 1 Hour Per unit of Item A= 12 Hours	100	88 Hours

If Maximum added capacity of cutting stage of 4 Hours is used to produce B

Total of 4 Units of Item B can be produced (4 Hours/ cutting Hours required to produce Item B) (4/1)= 4 Units

Total Profit would be (12UNITS *20000 USD +4UNITS*16000 USD)= USD 3,04,000/-

If only Item B is produced total profit would be 25Units OF ITEM B as calculated in Part 1 * 16000USD profit contribution per Unit OF ITEM B = 4,00,000 USD

AS PRODUCING ITEM B IS MORE PROFITABLE WE WOULD ARRIVE AT THE BEST POSSIBLE MIX BY REDUCING 1 UNIT OF B AND ADDING THE POSSIBLE MANUFACTURING OF UNITS OF A IN EXCESS HOURS OF ASSEMBLING.

BEST PRODUCTION MIX OF ITEM A AND ITEM B

                                                        POSSIBLE PRODUCTION MIX ON BASIS OF AVAILABLE CAPACITY HOURS

ITEM B UNITS IN NUMBER	25	24	23
ITEM A UNITS IN EXCESS HOURS	0	4	8

TOTAL CONTRIBUTION    IN USD                              4,00,000     4,64,000   5,28,000

(iTEM B*16000+ITEM A*20000)

THE BEST POSSIBLE MIX IS 23 UNITS OF ITEM B AND 8 UNITS OF ITEM A.

% FOR EACH STAGE        A                          B                                    TOTAL CAPACITY USED            % OF CAPACITY USED

CUTTING                   8*8=64 HOURS        23*1=23 HOURS                  64+23=87 HOURS                          87/100*100=87%

COATING    8*1=8HOURS 23*1=23HOURS                   23+8=31 HOURS                    31/50HOURS*100=62%

ASSEMBLING          8*1=8 HOURS          23*4=92 HOURS                   8+92=100 HOURS                  100/100*100= 100%