Question

QUESTION 6 to produces a total of 100 no. 15 kW and 25 kW diesel generators a day, using a tota of 240 man hours per day. It takes 2 man hours to produce a 15 kW and 4 man hours to produce a 25 kW diesel generator. The profit on a 15 kW generator is N5,000 while the profit on a 25 kW generator is N8,000. (i) Calculate the mix of the two sizes of generators the company must produce for maximum profit [10 Marks] (ii) What is the profit? 15 Marks] (1) Prove that it is the maximum profit achievable 15 Marks]

Answer 1

Solution (i):

S.No	Product	15KW	25KW
1	Profit/unit	5000	8000
2	Man hrs per unit	2	4
3	profit per man hour(1/2)	2500	2000
4	Rank (maximum profit)	1	2
5	Man hour allocation	240	0
6	No of units produced (5/2)	120	0
7	Profit earned (6*1)	600000	0

The best product mix for earning maximum profit is 120 number of 15kw generators and zero 25kw generators if there is no conditions for producing minimum number of either of the generators. With the available man hours wihich is a restricted resource, all the 240 man hours to be used for producing 15kw generators to earn a profit of 600000.

Solution (ii): The profit earned as above is 600000.

Solution iii: If 25kw generators alone are produced then profit earned is

(240/4)*8000=480000

If 15kw generators alone are produced then the profit earned is

(240/2)*5000=600000

If we produce both in any other combination, then the profit will range in between 480000 and 600000. Hence the mix as obtained in solution(i) above is the best yielding one.