a company manufactures a toy at a cost of Rm2 per unit and sells them for Rm x per unit.if the number sold is 800/x^2 per month,find the value of x for which the company could expect to maximise its monthly profit.

Answer 1

profit = revenue - cost
revenue = price * quantity = 800/x^2 * x = 800/x
cost = 2 * quantity = 2 * 800/x^2

p = 800/x - 1600/x^2
dp/dx = -800/x^2 + 3200/x^3 = 800/x^3(4-x)

So, maximum profit when charging Rm4/unit.

sales: 50
profit: 100