Question

Country Motorbikes Incorporated finds that it costs $400 to produce each motorbike, and that fixed costs are $1600 per day. The price function is p(x) = 700 − 5x, where p is the price (in dollars) at which exactly x motorbikes will be sold. Find the quantity Country Motorbikes should produce and the price it should charge to maximize profit. Also find the maximum profit.my equation for profit keeps on giving me a wrong answerquantity = 30price = 550profit =_________ ?

Answer 1

Answer:

30units,2900

Step-by-step explanation:

Given that Country Motorbikes Incorporated finds that it costs $400 to produce each motorbike, and that fixed costs are $1600 per day.

The price function is p(x) = 700 − 5x, where p is the price (in dollars) at which exactly x motorbikes will be sold.

If x units are produced and sold we have

Costs for x units = variable costs *x +Fixed costs $= 400x+1600$

Sales revenue = no of units sold * price = $x(700-5x) = 700x-5x^2$

Profit funciton = P(x) = Sales revenue - Total cost

= $700x-5x^2-400x-1600\\=300x-5x^2-1600$

To get maximum profit we use derivative test I derivative =0 and II derivative =negative

$P'(x) = 300-10x\\p"(x) = -10$

Producing 30 units will maximize the profit.

Max profit

=P(30) = 2900