Linear Cost and Revenue Functions (3.11.2)

Question 1

• Linear functions can be used to model many real-world situations, such as the cost, revenue, and profit for a company
manufacturing a product.
• Cost (C) is the amount of money a company must spend to manufacture its product(s).
• Revenue (R) is the amount of money the company receives from selling its product(s).
• Profit (P) is the company’s net gain: profit = revenue - cost.

Answer 1

• Linear functions can be used to model many real-world situations, such as the cost, revenue, and profit for a company
manufacturing a product.
• Cost (C) is the amount of money a company must spend to manufacture its product(s).
• Revenue (R) is the amount of money the company receives from selling its product(s).
• Profit (P) is the company’s net gain: profit = revenue - cost.

Question 2

Linear functions are applicable to many real-world
situations.
For example, the cost, revenue, and profit for a company
manufacturing a product can be modeled by linear functions.
Given the cost and revenue functions R(x) and C(x), the profit
function is the difference:
P(x) = R(x) – C(x).
Applying that profit function to a business problem, you can
determine potential profit given a specific number of planes
to be produced.
Just plug in the number of planes produced into P(x). The
result is the profit.
What if only 20 planes are produced?
Plugging into the profit function results in –$8,690.
A negative profit means the company will experience a
loss. The company will probably choose to avoid a loss and
produce more than 20 planes.
You can also find the break-even point, or the point where
the profit is exactly equal to zero. At the break-even point,
the company is not gaining or losing any money.
To find where the profit equals zero, set P(x) equal to zero
and solve for x.

Answer 2

Linear functions are applicable to many real-world
situations.
For example, the cost, revenue, and profit for a company
manufacturing a product can be modeled by linear functions.
Given the cost and revenue functions R(x) and C(x), the profit
function is the difference:
P(x) = R(x) – C(x).
Applying that profit function to a business problem, you can
determine potential profit given a specific number of planes
to be produced.
Just plug in the number of planes produced into P(x). The
result is the profit.
What if only 20 planes are produced?
Plugging into the profit function results in –$8,690.
A negative profit means the company will experience a
loss. The company will probably choose to avoid a loss and
produce more than 20 planes.
You can also find the break-even point, or the point where
the profit is exactly equal to zero. At the break-even point,
the company is not gaining or losing any money.
To find where the profit equals zero, set P(x) equal to zero
and solve for x.