A manufacturer of DVD players has weekly fixed costs of $1,570 and variable costs of $13.50 per unit for one particular model. The company sells this model to dealers for $20.50 each.

(a) For this model DVD player, write the function for weekly total costs C(x).
C(x) =

(b) Write the function for total revenue R(x).
R(x) =

(c) Write the function for profit P(x).
P(x) =

(d) Find C(200).

C(200) =

Interpret C(200). (Multiple Choice)

A. This is the cost (in dollars) of producing 200 DVD players.

B. For every additional DVD player produced the cost increases by this much.

C. When this many DVD players are produced the cost is $200.

D. For each $1 increase in cost this many more DVD players can be produced.

Find R(200).

R(200) =

Interpret R(200). (Multiple Choice)

A. When this many DVD players are produced the revenue generated is $200.

B. For each $1 increase in revenue this many more DVD players can be produced.

C. For every additional DVD player produced the revenue generated increases by this much.

D. This is the revenue (in dollars) generated from the sale of 200 DVD players.

Find P(200).

P(200) =

Interpret P(200). (Multiple Choice)

A. This is the profit (in dollars) when 200 DVD players are sold, and since it is positive it means that the company makes money when 200 DVD players are sold.

B. This is the profit (in dollars) when 200 DVD players are sold, but since it is negative it means that the company loses money when 200 DVD players are sold.

C. For each additional DVD player sold the profit (in dollars) increases by this much, but since it is negative it means that the company needs to decrease the number of DVD players sold in order to make a profit.

D. For each additional DVD player sold the profit (in dollars) increases by this much, but since it is positive it means that the company is producing too many DVD players.

(e) Find C(400).

C(400) =

Interpret C(400). (Multiple Choice)

A. For each $1 increase in cost this many more DVD players can be produced.

B. For every additional DVD player produced the cost increases by this much.

C. When this many DVD players are produced the cost is $400.

D. This is the cost (in dollars) of producing 400 DVD players.

Find R(400).

R(400) =

Interpret R(400). (Multiple Choice)

A. When this many DVD players are produced the revenue generated is $400.

B. For each $1 increase in revenue this many more DVD players can be produced.

C. For every additional DVD player produced the revenue generated increases by this much.

D. This is the revenue (in dollars) generated from the sale of 400 DVD players.

Find P(400).

P(400) =

Interpret P(400). (Multiple Choice)

A. For each additional DVD player sold the profit (in dollars) increases by this much, but since it is negative it means that the company needs to decrease the number of DVD players sold in order to make a profit.

B. For each additional DVD player sold the profit (in dollars) increases by this much, but since it is positive it means that the company is producing too many DVD players.

C. This is the profit (in dollars) when 400 DVD players are sold, but since it is negative it means that the company loses money when 400 DVD players are sold.

D. This is the profit (in dollars) when 400 DVD players are sold, and since it is positive it means that the company makes money when 300 DVD players are sold.

(f) Find the marginal profit
MP.

MP =

Write a sentence that explains its meaning.(Multiple Choice)
A. When revenue is increased by this much the profit is increased by $1.

B. When costs are decreased by this much the profit is increased by $1.

C. For each $1 increase in profit this many more DVD players can be produced.

D. Each additional DVD player sold increases the profit by this many dollars.

Question

A manufacturer of DVD players has weekly fixed costs of $1,570 and variable costs of $13.50 per unit for one particular model. The company sells this model to dealers for $20.50 each.

(a) For this model DVD player, write the function for weekly total costs C(x).
C(x) =

(b) Write the function for total revenue R(x).
R(x) =

(c) Write the function for profit P(x).
P(x) =

(d) Find C(200).

C(200) =

Interpret C(200). (Multiple Choice)

A. This is the cost (in dollars) of producing 200 DVD players.

B. For every additional DVD player produced the cost increases by this much.

C. When this many DVD players are produced the cost is $200.

D. For each $1 increase in cost this many more DVD players can be produced.

Find R(200).

R(200) =

Interpret R(200). (Multiple Choice)

A. When this many DVD players are produced the revenue generated is $200.

B. For each $1 increase in revenue this many more DVD players can be produced.

C. For every additional DVD player produced the revenue generated increases by this much.

D. This is the revenue (in dollars) generated from the sale of 200 DVD players.

Find P(200).

P(200) =

Interpret P(200). (Multiple Choice)

A. This is the profit (in dollars) when 200 DVD players are sold, and since it is positive it means that the company makes money when 200 DVD players are sold.

B. This is the profit (in dollars) when 200 DVD players are sold, but since it is negative it means that the company loses money when 200 DVD players are sold.

C. For each additional DVD player sold the profit (in dollars) increases by this much, but since it is negative it means that the company needs to decrease the number of DVD players sold in order to make a profit.

D. For each additional DVD player sold the profit (in dollars) increases by this much, but since it is positive it means that the company is producing too many DVD players.

(e) Find C(400).

C(400) =

Interpret C(400). (Multiple Choice)

A. For each $1 increase in cost this many more DVD players can be produced.

B. For every additional DVD player produced the cost increases by this much.

C. When this many DVD players are produced the cost is $400.

D. This is the cost (in dollars) of producing 400 DVD players.

Find R(400).

R(400) =

Interpret R(400). (Multiple Choice)

A. When this many DVD players are produced the revenue generated is $400.

B. For each $1 increase in revenue this many more DVD players can be produced.

C. For every additional DVD player produced the revenue generated increases by this much.

D. This is the revenue (in dollars) generated from the sale of 400 DVD players.

Find P(400).

P(400) =

Interpret P(400). (Multiple Choice)

A. For each additional DVD player sold the profit (in dollars) increases by this much, but since it is negative it means that the company needs to decrease the number of DVD players sold in order to make a profit.

B. For each additional DVD player sold the profit (in dollars) increases by this much, but since it is positive it means that the company is producing too many DVD players.

C. This is the profit (in dollars) when 400 DVD players are sold, but since it is negative it means that the company loses money when 400 DVD players are sold.

D. This is the profit (in dollars) when 400 DVD players are sold, and since it is positive it means that the company makes money when 300 DVD players are sold.

(f) Find the marginal profit

MP.

MP =

Write a sentence that explains its meaning.(Multiple Choice)

A. When revenue is increased by this much the profit is increased by $1.

B. When costs are decreased by this much the profit is increased by $1.

C. For each $1 increase in profit this many more DVD players can be produced.

D. Each additional DVD player sold increases the profit by this many dollars.