Question

The cost function for producing x items is C(x) =
45000 + 25x - 0.10x^2. The revenue function R(x) = 750 -
0.60x^2.

a.Determine the production cost for the first 500 items.

b.The marginal cost function.

c.How fast is the cost growing when production is at 500
units.

d.The average cost per item for the first 500 items.

e.The marginal revernue function R'(x).

f.The profit function.

g.The marginal profit function.

h.What production level maximizes revenue.

Answer #1

Answers.

The revenue function of a company is given by
R(x)=-2x^2+25x+150, the cost function is given by C(x)=13x+100
a. Find the marginal cost and marginal revenue function.
b. Find the production level x where the profit is maximized.
Then find the maximum profit.

Consider that for ‘x’ units
sold, the total REVENUE function is : R(x) =
75x2– 15x
– 200 and the total COST function is :
C(x) = 750 + 25x –
100 √ x.
(b)
Also determine values of (i) Marginal Revenue when x= 25
and (ii) MP(25), where marginal Revenue is
defined as derivative of Revenue function and MP(x) =
P'(x).

7. Suppose the cost, in dollars, of producing x items is given
by the function C(x) = 1/6x3+ 2x2+ 30.
Current production is at x = 9 units.
(a) (3 points) Use marginal analysis to find the marginal cost
of producing the 10th unit.
(b) (3 points) Find the actual cost of producing the 10th
unit.

3) The marginal cost for producing x items can be given by the
formula: C ′ ( x ) = 350 − 0.18 x. Find the total cost function if
the cost of making 300 items is known to be $97,400.
a) What are the fixed costs?
b) How much would it cost to make 500 items?

If C(x) = 14000 +
600x − 0.6x2 +
0.004x3 is the cost function and
p(x) = 1800 −
6x is the demand function, find the production
level that will maximize profit. (Hint: If the profit is maximized,
then the marginal revenue equals the marginal cost.)

The cost of producing a plastic toy is given by the function
C(x) = 8x + 25, where x is the number of hundreds of toys. The
revenue from toy sales is given by R(x) = −x2 + 120x − 360. Since
profit = revenue − cost, the profit function must be P(x) = −x2 +
112x − 385 (verify). How many toys sold will produce the maximum
profit? What is the maximum profit?

A
shoe company sells x shoes at price p = 500-x. The cost for
production is c = 2000 + 10x^2.
a. what is the marginal revenue of the 50th order?
b. what is the breakeven point?
c. what production maximizes total profit?
d. what price maximizes profit?

If a company's cost function for a product is
C(q) = 2280 + 3.8q + 0.004q2
and the revenue function is
R(q) = 12.2q − 0.002q2,
find the production level that maximizes profit.
................................. units

Cost, revenue, and profit are in dollars and x is the
number of units.
Suppose that the total revenue function for a product is
R(x) =
55x
and that the total cost function is
C(x) = 2200 +
35x + 0.01x2.
(a) Find the profit from the production and sale of 500
units.
(b) Find the marginal profit function
(c) Find MP at x = 500.
Explain what it predicts.
The total profit will ------ by approximately $------- on the...

The revenue from selling q items is R(q)=650q−q^2, and the total
cost is C(q)=100+11q. Write a function that gives the total profit
earned, and find the quantity which maximizes the profit.
Profit π(q)=
Quantity maximizing profit q=

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