Math Is Fun Forum

mathland

Member

Registered: 2021-03-25

Posts: 444

Business Application

A roofing contractor purchases a shingle delivery truck with a shingle
elevator for $42,000. The vehicle requires an average expenditure of $9.50 per hour for fuel and maintenance, and the operator is paid $11.50 per hour.

(a) Write a linear equation giving the total cost C of operating this equipment for t hours. (Include the purchase cost of the equipment.)

I must add 9.50 + 11.50 to get 21

I then multiply 21 times t.

I finally add 21t to 42,000.

My equation is C(t) = 42,000 + 21t.

Is this correct?

(b) Assuming that customers are charged $45 per hour of machine use, write an equation for the revenue R
obtained from t hours of use.

I know the revenue formula is
Revenue = Quantity × Price.

I say the formula is R = 45t.

Is this right?

(c) Use the formula for profit P = R − C to write an equation for the profit obtained from t hours of use.

If R = 45t, and C = 42,000, I say the equation needed is P = 45t - 42,000.

Is this right?

(d) Use the result of part (c) to find the break-even point—that is, the number of hours this equipment
must be used to yield a profit of 0 dollars.

I am not too sure about part (d). What is break-even in the business world?

Thanks.

Mathegocart

Member

Registered: 2012-04-29

Posts: 2,226

Re: Business Application

A roofing contractor purchases a shingle delivery truck with a shingle
elevator for $42,000. The vehicle requires an average expenditure of $9.50 per hour for fuel and maintenance, and the operator is paid $11.50 per hour.

(a) Write a linear equation giving the total cost C of operating this equipment for t hours. (Include the purchase cost of the equipment.)

I must add 9.50 + 11.50 to get 21

I then multiply 21 times t.

I finally add 21t to 42,000.

My equation is C(t) = 42,000 + 21t.

Is this correct?

(b) Assuming that customers are charged $45 per hour of machine use, write an equation for the revenue R
obtained from t hours of use.

I know the revenue formula is
Revenue = Quantity × Price.

I say the formula is R = 45t.

Is this right?

(c) Use the formula for profit P = R − C to write an equation for the profit obtained from t hours of use.

If R = 45t, and C = 42,000, I say the equation needed is P = 45t - 42,000.

Is this right?

(d) Use the result of part (c) to find the break-even point—that is, the number of hours this equipment
must be used to yield a profit of 0 dollars.

I am not too sure about part (d). What is break-even in the business world?

Thanks.

(a) You betcha.

(b) Yup.

(c) Well, there might be a typo here. R = 45t and C = (21t + 42000). So R - C = 24t - 42,000.

(d) Find the number of hours(t) that it takes for revenue to meet costs; i.e, when does R - C = 0?

---

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He will be sorely missed.

mathland

Member

Registered: 2021-03-25

Posts: 444

Re: Business Application

A roofing contractor purchases a shingle delivery truck with a shingle
elevator for $42,000. The vehicle requires an average expenditure of $9.50 per hour for fuel and maintenance, and the operator is paid $11.50 per hour.

(a) Write a linear equation giving the total cost C of operating this equipment for t hours. (Include the purchase cost of the equipment.)

I must add 9.50 + 11.50 to get 21

I then multiply 21 times t.

I finally add 21t to 42,000.

My equation is C(t) = 42,000 + 21t.

Is this correct?

(b) Assuming that customers are charged $45 per hour of machine use, write an equation for the revenue R
obtained from t hours of use.

I know the revenue formula is
Revenue = Quantity × Price.

I say the formula is R = 45t.

Is this right?

(c) Use the formula for profit P = R − C to write an equation for the profit obtained from t hours of use.

If R = 45t, and C = 42,000, I say the equation needed is P = 45t - 42,000.

Is this right?

(d) Use the result of part (c) to find the break-even point—that is, the number of hours this equipment
must be used to yield a profit of 0 dollars.

I am not too sure about part (d). What is break-even in the business world?

Thanks.

(a) You betcha.

(b) Yup.

(c) Well, there might be a typo here. R = 45t and C = (21t + 42000). So R - C = 24t - 42,000.

(d) Find the number of hours(t) that it takes for revenue to meet costs; i.e, when does R - C = 0?

What is wrong with part (c)?