Question

a utilities company sells electrical wiring at $7 per 15 meters, which costs them $3 per 15 meters. if a customer purchases at least 300 meters, the company offers a 10% discount with an additional 5% discount for every 300 additional meters, such that 650 meters would receive a discount of a 15%. They must sell less than what length of wire if they wish to have at least a 40% profit margin?

Answer 1

Answer:

Cost per meter = $3

To earn 40% profit margin minimum price required is = 3 / (1 - 40%) = $5 per meter.

As such maximum discount per meter the company can give = $7 - $5 = $2 per meter.

Maximum discount in terms of % = 2/ 7 = 28.57%

As discount slab is 5% maximum discount the company can give is 25%.

If a customer purchases at least 300 meters, the company offers a 10% discount with an additional 5% discount for every 300 additional meters.

Each additio Total 300 First Electrical wiring (in meters) Discount 1,200 25% 300 10% 300 300 5% 5% 5%

As such 25% discount will be applicable for sale starting 1,200 meters up to 1,499 meters.

To ensure no more than 25% discount the company must sell less than 1499 meters.

As such the company must sell less than 1,499 meters of wire if it wishes to have at least a 40% profit margin