A manufacturer of DVD players has monthly fixed costs of $9900 and variable costs of $60 per unit for one particular model. The company sells this model to dealers for $100 each.

(a) For this model DVD player, write the function for monthly 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(240).

C(240) =

Interpret C(240).

For each $1 increase in cost this many more DVD players can be produced.This is the cost (in dollars) of producing 240 DVD players. When this many DVD players are produced the cost is $240.For every additional DVD player produced the cost increases by this much.

Find R(240).

R(240) =

Interpret R(240).

This is the revenue (in dollars) generated from the sale of 240 DVD players.When this many DVD players are produced the revenue generated is $240. For every additional DVD player produced the revenue generated increases by this much.For each $1 increase in revenue this many more DVD players can be produced.

Find P(240).

P(240) =

Interpret P(240).

This is the profit (in dollars) when 240 DVD players are sold, but since it is negative it means that the company loses money when 240 DVD players are sold.This is the profit (in dollars) when 240 DVD players are sold, and since it is positive it means that the company makes money when 240 DVD players are sold. 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.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(390).

C(390) =

Interpret C(390).

When this many DVD players are produced the cost is $390.For every additional DVD player produced the cost increases by this much. This is the cost (in dollars) of producing 390 DVD players.For each $1 increase in cost this many more DVD players can be produced.

Find R(390).

R(390) =

Interpret R(390).

When this many DVD players are produced the revenue generated is $390.This is the revenue (in dollars) generated from the sale of 390 DVD players. For every additional DVD player produced the revenue generated increases by this much.For each $1 increase in revenue this many more DVD players can be produced.

Find P(390).

P(390) =

Interpret P(390).

This is the profit (in dollars) when 390 DVD players are sold, but since it is negative it means that the company loses money when 390 DVD players are sold.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. This is the profit (in dollars) when 390 DVD players are sold, and since it is positive it means that the company makes money when 300 DVD players are sold.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.

(f) Find the marginal profit

MP.

MP =

Write a sentence that explains its meaning.

Each additional DVD player sold increases the profit by this many dollars.For each $1 increase in profit this many more DVD players can be produced. When costs are decreased by this much the profit is increased by $1.When revenue is increased by this much the profit is increased by $1.