Extreme Protection, Inc. manufactures helmets for skiing and snowboarding. The fixed costs for one model of helmet are $7800 per month. Materials and labor for each helmet of this model are $35, and the company sells this helmet to dealers for $70 each. (Let x represent the number of helmets sold. Let C, R, and P be measured in dollars.)

(a) For this helmet, 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(200).

C(200) =______________

Interpret C(200). Which one is the answer:

1. When this many helmets are produced the cost is $200.

2. For every additional helmet produced the cost increases by this much.

3. This is the cost (in dollars) of producing 200 helmets.

4. For each $1 increase in cost this many more helmets can be produced.

Find R(200).

R(200) =__________

Interpret R(200). Which one is the answer:

1. For every additional helmet produced the revenue generated increases by this much.

2. When this many helmets are produced the revenue generated is $200.

3. For each $1 increase in revenue this many more helmets can be produced.

4. This is the revenue (in dollars) generated from the sale of 200 helmets.

Find P(200).

P(200) =___________

Interpret P(200). Which one is the answer:

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

2. For each additional helmet 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 helmets sold in order to make a profit.

3. For each additional helmet sold the profit (in dollars) increases by this much, but since it is positive it means that the company is producing too many helmets.

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

(e) Find C(300).

C(300) =_____________

Interpret C(300). Which one is the answer:

1. When this many helmets are produced the cost is $300.

2. This is the cost (in dollars) of producing 300 helmets.

3. For each $1 increase in cost this many more helmets can be produced.

4. For every additional helmet produced the cost increases by this much.

Find R(300).

R(300) =________

Interpret R(300). Which one is the answer:

1. For each $1 increase in revenue this many more helmets can be produced.

2. When this many helmets are produced the revenue generated is $300.

3. For every additional helmet produced the revenue generated increases by this much.

4. This is the revenue (in dollars) generated from the sale of 300 helmets.

Find P(300).

P(300) =_______

Interpret P(300). Which one is the answer:

1. This is the profit (in dollars) when 300 helmets are sold, and since it is positive it means that the company makes money when 300 helmets are sold.

2. For each additional helmet sold the profit (in dollars) increases by this much, but since it is positive it means that the company is producing too many helmets.

3. This is the profit (in dollars) when 300 helmets are sold, but since it is negative it means that the company loses money when 300 helmets are sold.

4. For each additional helmet 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 helmets sold in order to make a profit.

(f) Find the marginal profit
MP.

MP =________

Write a sentence that explains its meaning. Which one is the answer:

1. Each additional helmet sold increases the profit by this many dollars.

2. For each $1 increase in profit this many more helmets can be produced.

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

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

Question

Extreme Protection, Inc. manufactures helmets for skiing and snowboarding. The fixed costs for one model of helmet are $7800 per month. Materials and labor for each helmet of this model are $35, and the company sells this helmet to dealers for $70 each. (Let x represent the number of helmets sold. Let C, R, and P be measured in dollars.)

(a) For this helmet, 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(200).

C(200) =______________

Interpret C(200). Which one is the answer:

1. When this many helmets are produced the cost is $200.

2. For every additional helmet produced the cost increases by this much.

3. This is the cost (in dollars) of producing 200 helmets.

4. For each $1 increase in cost this many more helmets can be produced.

Find R(200).

R(200) =__________

Interpret R(200). Which one is the answer:

1. For every additional helmet produced the revenue generated increases by this much.

2. When this many helmets are produced the revenue generated is $200.

3. For each $1 increase in revenue this many more helmets can be produced.

4. This is the revenue (in dollars) generated from the sale of 200 helmets.

Find P(200).

P(200) =___________

Interpret P(200). Which one is the answer:

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

2. For each additional helmet 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 helmets sold in order to make a profit.

3. For each additional helmet sold the profit (in dollars) increases by this much, but since it is positive it means that the company is producing too many helmets.

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

(e) Find C(300).

C(300) =_____________

Interpret C(300). Which one is the answer:

1. When this many helmets are produced the cost is $300.

2. This is the cost (in dollars) of producing 300 helmets.

3. For each $1 increase in cost this many more helmets can be produced.

4. For every additional helmet produced the cost increases by this much.

Find R(300).

R(300) =________

Interpret R(300). Which one is the answer:

1. For each $1 increase in revenue this many more helmets can be produced.

2. When this many helmets are produced the revenue generated is $300.

3. For every additional helmet produced the revenue generated increases by this much.

4. This is the revenue (in dollars) generated from the sale of 300 helmets.

Find P(300).

P(300) =_______

Interpret P(300). Which one is the answer:

1. This is the profit (in dollars) when 300 helmets are sold, and since it is positive it means that the company makes money when 300 helmets are sold.

2. For each additional helmet sold the profit (in dollars) increases by this much, but since it is positive it means that the company is producing too many helmets.

3. This is the profit (in dollars) when 300 helmets are sold, but since it is negative it means that the company loses money when 300 helmets are sold.

4. For each additional helmet 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 helmets sold in order to make a profit.

(f) Find the marginal profit

MP.

MP =________

Write a sentence that explains its meaning. Which one is the answer:

1. Each additional helmet sold increases the profit by this many dollars.

2. For each $1 increase in profit this many more helmets can be produced.

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

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