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 = ?

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

Sales revenue = no of units sold * price =

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

=

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

Producing 30 units will maximize the profit.

Max profit

=P(30) = 2900

area of part 1:

a1=base*height/2=(8+2)*(8-2-2-1)/2=10*3/2=15 ft^2

area of part 2:

a2=length*width=(8+2)*1=10 ft2

area of part 3:

a3=length*width=8*2=16 ft2

total shaded area : a1+a2+a3=41 ft2

total area of the reactangle : a=16*8=128 ft2

total area of the nonshaded region : 128-41=87 ft2