Question

The Pear company sells pPhones. The cost to manufacture x pPhones is C ( x ) = - 21 x² + 67000 x + 20006 dollars (this includes overhead costs and production costs for each pPhone). If the company sells x pPhones for the maximum price they can fetch, the revenue function will be R ( x ) = - 28 x² + 179000 x dollars.

How many pPhones should the pear company produce and sell to maximize profit? (remember that profit = revenue - cost)

Answer 1

Company should produce 8000 phones for the maximum profit.

Explanation:

Function representing cost to the manufacturer is,

C(x) = -21x²+ 67000x + 20006

Function that represents the revenue generated is,

R(x) = -28x² + 179000x

Function representing profit to the company,

Profit = Revenue generated - Cost price

= -28x² + 179000x - (- 21x² + 67000x + 20006)

= -28x² + 21x² + 179000x - 67000x - 20006

P(x) = -7x² + 112000x - 20006

Since this function is a quadratic function therefore, the maximum price generated will be for

`x=-(b)/(2a)`

From the given quadratic function, a = (-7), b = 112000 and c = -20006

Therefore, for
`x=-(112000)/(2* (-7))`

Or x = 8000 the profit to the company will be maximum.

That means pear company should produce 8000 phones for the maximum profit.