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 [tex]= 400x+1600[/tex]
Sales revenue = no of units sold * price = [tex]x(700-5x) = 700x-5x^2[/tex]
Profit funciton = P(x) = Sales revenue - Total cost
= [tex]700x-5x^2-400x-1600\\=300x-5x^2-1600[/tex]
To get maximum profit we use derivative test I derivative =0 and II derivative =negative
[tex]P'(x) = 300-10x\\p"(x) = -10<0\\x=30 whenP'(x) =0[/tex]
Producing 30 units will maximize the profit.
Max profit
=P(30) = 2900
