Math / Algebra

QuestionA company that manufactures small canoes has a fixed cost of $\$ 14,000$ . It costs $\$ 40$ to produce each canoe. The selling price is $\$ 80$ per canoe. (In solving this exercise, let $x$ represent the number of canoes produced and sold.) a. Write the cost function. $C(x)=14000+40 \cdot x \quad$ (Type an expression using $x$ as the variable.) b. Write the revenue function. $R(x)=$ $\square$ (Type an expression using $x$ as the variable.)

Studdy Solution

STEP 1

What is this asking? We need to figure out the equations for the total cost and total income of a canoe company based on how many canoes they make and sell. Watch out! Don't mix up cost and revenue!
Cost is how much the company spends, and revenue is how much money the company makes.

STEP 2

1. Define the cost function
2. Define the revenue function

STEP 3

Alright, let's break down the cost of making canoes!
There are two parts to this: the fixed cost and the variable cost.
The fixed cost is like the base cost that exists no matter how many canoes are made.
In this case, the fixed cost is \$14,000.
This could be the cost of renting the factory, paying the workers' salaries, or buying the machinery.

STEP 4

The variable cost depends on how many canoes are produced.
Each canoe costs \$40 to make.
So, if the company makes $x$ canoes, the variable cost is $40 \cdot x$ .

STEP 5

To get the total cost, we add the fixed cost and the variable cost together.
So, our cost function $C(x)$ is: $C(x) = 14000 + 40 \cdot x$ Where $C(x)$ represents the total cost of producing $x$ canoes.

STEP 6

Now, let's talk about revenue!
Revenue is the money the company makes from selling canoes.
They sell each canoe for \$80.

STEP 7

If they sell $x$ canoes, their revenue, $R(x)$ , is simply the price per canoe multiplied by the number of canoes sold: $R(x) = 80 \cdot x$ Where $R(x)$ represents the total revenue from selling $x$ canoes.

STEP 8

a. The cost function is $C(x) = 14000 + 40 \cdot x$ . b. The revenue function is $R(x) = 80 \cdot x$ .

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Studdy Solution

STEP 1

What is this asking? We need to figure out the equations for the total cost and total income of a canoe company based on how many canoes they make and sell. Watch out! Don't mix up cost and revenue!
Cost is how much the company spends, and revenue is how much money the company makes.

STEP 2

1. Define the cost function
2. Define the revenue function

STEP 3

STEP 4

The variable cost depends on how many canoes are produced.
Each canoe costs \$40 to make.
So, if the company makes $x$ canoes, the variable cost is $40 \cdot x$ .

STEP 5

To get the total cost, we add the fixed cost and the variable cost together.
So, our cost function $C(x)$ is: $C(x) = 14000 + 40 \cdot x$ Where $C(x)$ represents the total cost of producing $x$ canoes.

STEP 6

Now, let's talk about revenue!
Revenue is the money the company makes from selling canoes.
They sell each canoe for \$80.

STEP 7

If they sell $x$ canoes, their revenue, $R(x)$ , is simply the price per canoe multiplied by the number of canoes sold: $R(x) = 80 \cdot x$ Where $R(x)$ represents the total revenue from selling $x$ canoes.

STEP 8

a. The cost function is $C(x) = 14000 + 40 \cdot x$ . b. The revenue function is $R(x) = 80 \cdot x$ .

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Studdy Solution

STEP 1

What is this asking? We need to figure out the equations for the total cost and total income of a canoe company based on how many canoes they make and sell. Watch out! Don't mix up cost and revenue!Cost is how much the company spends, and revenue is how much money the company makes.

STEP 2

1. Define the cost function2. Define the revenue function

STEP 3

STEP 4

The variable cost depends on how many canoes are produced.Each canoe costs **\$40** to make.So, if the company makes xxx canoes, the variable cost is 40⋅x40 \cdot x40⋅x.

STEP 5

To get the *total* cost, we **add** the fixed cost and the variable cost together.So, our cost function C(x)C(x)C(x) is: C(x)=14000+40⋅xC(x) = 14000 + 40 \cdot xC(x)=14000+40⋅x Where C(x)C(x)C(x) represents the total cost of producing xxx canoes.

STEP 6

Now, let's talk about revenue!Revenue is the money the company makes from selling canoes.They sell each canoe for **\$80**.

STEP 7

If they sell xxx canoes, their revenue, R(x)R(x)R(x), is simply the price per canoe multiplied by the number of canoes sold: R(x)=80⋅xR(x) = 80 \cdot xR(x)=80⋅x Where R(x)R(x)R(x) represents the total revenue from selling xxx canoes.

STEP 8

a. The cost function is C(x)=14000+40⋅xC(x) = 14000 + 40 \cdot xC(x)=14000+40⋅x. b. The revenue function is R(x)=80⋅xR(x) = 80 \cdot xR(x)=80⋅x.

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Studdy solves anything!

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

What is this asking? We need to figure out the equations for the total cost and total income of a canoe company based on how many canoes they make and sell. Watch out! Don't mix up cost and revenue!
Cost is how much the company spends, and revenue is how much money the company makes.

1. Define the cost function
2. Define the revenue function

The variable cost depends on how many canoes are produced.
Each canoe costs \$40 to make.
So, if the company makes $x$ canoes, the variable cost is $40 \cdot x$ .

To get the total cost, we add the fixed cost and the variable cost together.
So, our cost function $C(x)$ is: $C(x) = 14000 + 40 \cdot x$ Where $C(x)$ represents the total cost of producing $x$ canoes.

Now, let's talk about revenue!
Revenue is the money the company makes from selling canoes.
They sell each canoe for \$80.

If they sell $x$ canoes, their revenue, $R(x)$ , is simply the price per canoe multiplied by the number of canoes sold: $R(x) = 80 \cdot x$ Where $R(x)$ represents the total revenue from selling $x$ canoes.

a. The cost function is $C(x) = 14000 + 40 \cdot x$ . b. The revenue function is $R(x) = 80 \cdot x$ .