1)A firm has monthly average costs, in dollars, given by the following function
ID: 2828779 • Letter: 1
Question
1)A firm has monthly average costs, in dollars, given by the following function where x is the number of units produced per month.
C =
+ 200 + x
The firm can sell its product in a competitive market for $1500 per unit. If production is limited to 100 units per month, find the number of units that gives maximum profit, and find the maximum profit.
2)If the total cost function for a product is
C(x) = 6(x + 3)3
dollars, where x represents the number of hundreds of units produced, producing how many units will minimize average cost?
3)The weekly demand function for x units of a product sold by only one firm is
p = 200 ?1/2
and the average cost of production and sale is x dollars,
C = 100 + 2x dollars.
(a) Find the quantity that will maximize profit.
(b) Find the selling price at this optimal quantity.
(c) What is the maximum profit?
38,000 xExplanation / Answer
3800/x+200+x = 1500X
-3800x^-2+1=0
x= sqrt(3800) = 62 products
minimum cost
maximum profit
2)
C(x) = 6(x + 3)3
average cost = c(x)/x
= 6(x+3)^3/x
9x^2+2x^3-27 =0
x= 3/2 = 1.5 = 1500 units
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