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koban [17]
3 years ago
8

Suppose that when the price of a certain commodity is p dollars per unit, then x hundred units will be purchased by consumers, w

here p 0.05x 38. the cost of producing x hundred units is c(x) 0.02x 2 3x 574.77 hundred dollars. sobecki, dave; price, michael; hoffmann, laurence; bradley, gerald. applied calculus for business, economics, and the social and life sciences, expanded edition, 11th edition (page 28). mcgraw-hill higher education -a. kindle edition.
Business
1 answer:
Nataly_w [17]3 years ago
7 0

Answer:

Profit = TR- TC
= x (P) - C(x)
= x(-0.05x+38) - (0.02x^{2} + 3x + 574.77)
= -0.05x^{2} + 38x - 0.02x^{2} - 3x - 574.77
= -0.07x^{2} + 35x -574.77

This profit equation is an equation of a parabola that opens downward (Since A=-0.07<0) and has its vertex at

x= -\frac{B}{2A}  = -\frac{35}{2 (-0.07)}  = 250

Thus, revenue is maximized when x=250 hundred units. At this quantity maximum profit is

P(250)=3800.23 hundred dollars

b. Profits are maximised at x=250 hundred units. The per unit price at this is,

p= -0.05x + 38&#10;= -0.05 (250) + 38&#10;= $25.5


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