Question

A manufacturer of concentrated liquid detergent sells 60% of its product in consumer markets and the rest in institutional markets. Its institutional buyers pay a price of $12 per gallon which is 75% of the price paid by its consumer buyers. Additional information available about the company is as below:

Variable cost = 8 $/Gallon, Fixed cost = 40,000 $/month.

Presently, the company makes a profit of 12,500 $/m.

If the company is considering offering a 10% price reduction as a promotion to all buyers, how much additional sales in Gallons per month must it achieve so that its present profit level is maintained?

Answer 1

Let x be the current quanitty sold
x*60%*12+x*(1-60%)*12*75%-x*8-40000=12500
x=(12500+40000)/(60%*12+(1-60%)*12*75%-8)
=>x=18750.00000

Let new quantity sold be y
y*60%*12*(1-10%)+y*(1-60%)*12*75%*(1-10%)-y*8-40000=12500
=>y=(12500+40000)/(60%*12*(1-10%)+(1-60%)*12*75%*(1-10%)-8)
=>y=30523.25581

Hence,

additional sales=30524-18750=11774 gallons per month

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