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AlekseyPX
3 years ago
11

Suppose that each day a company has fixed costs of 400 dollars and variable costs of 0.8x+1420 dollars per unit, where x is the

number of units produced that day. Suppose further that the selling price of its product is 1500−0.25x dollars per unit.
a) each day, the company breaks even at production levels (blank) units
b) the maximum daily revenue attained is (blank) dollars
c) the price that maximizes profit is (blank) dollars per unit
Mathematics
1 answer:
Bess [88]3 years ago
5 0

Answer:

Step-by-step explanation:

Given that a company fixed costs are 400 dollars

and variable cost = 0.8x+1420 per unit and x the no of units produced

Selling price = 1500-0.25x per unit

a) Break even units

At break even units selling price = variable cost

1500-0.25x=0.8x+1420\\1.05x = 80\\x=76.19~76

Break even units = 76

b) Revenue = Sales - total costs

= x(1500-0.25x)-(x)(0.8x+1420)-400\\= 1500x-0.25x^2-0.8x^2-1420x-400\\= -1.05x^2+80x-400

Use derivative test to get max revenue

R'(x) = -2.10x+80

R"(X) <0

So maximum when I derivative =0 or when

x=38.10

x=38

c) price when x =38 is

P = 1500-0.25(38)\\=1490.5

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