Please give me step by step solution. Thank you! PROFIT suppose that when the pr
ID: 3004903 • Letter: P
Question
Please give me step by step solution. Thank you!
PROFIT suppose that when the price of a certain commodity is a p dollar per unit, then x hundred units will be purchased by consumers, where p= -0.05x + 38. The cost of producing x hundred units is C(x) = 0.02x square + 3x + 574.77 hundred dollars.
a. Express the profit P obtained from the sale of x. Sketch the graph of the profit function
b. find the average profit AP when the price is $37 per unit
c. Use the profit curve found in part (a) to determine the level of production x that result in maximum profit. What unit price p correspond to maximum profit
Explanation / Answer
a) Profit = Revenue - Cost
= price * qty - cost
= pq - c(x)
= (-.05x + 38)*x - (.02x2 + 3x + 574.77)
= (-5x + 38)100x - (.02*10000x2 + 300x + 574.77)
= -500x^2 + 3800x -200x^2 - 300x - 574.77 = -700x2 + 3500x -574.77
b) When p = 37, 37 = -5x + 38 or x = 20 Units (.2 hundered to be precise)
Profit = $97.23. AP = Profit/Unit = 97.23/20 = 4.8615
c) Profit is maximum when P'(x) = 0
In other words, -1400x + 3500 = 0 or x = 2.5 hundred = 250 Units
p = -.05*250 + 38 = $25.5/ unit