Khadija is in the business of manufacturing phones. She must pay a daily fixed cost to rent the building and equipment, and also pays a cost per phone produced for materials and labor. The labor and materials cost $150 for each phone manufactured, and the total cost of producing 8 phones in a day would be $1800. Write an equation for C, comma*C*, in terms of p, comma*p*, representing total cost, in dollars, of producing p*p* phones in a given day.

To find an equation for the total cost $ C $ of producing $ p $ phones in a day, we can break down the costs into two parts: the fixed cost and the variable cost.

1. **Fixed cost**: This is a constant amount Khadija must pay each day, regardless of how many phones are produced. We'll call this $ F $ (fixed cost), which we need to determine.
  
2. **Variable cost**: This is the cost per phone produced, which is given as $150 per phone. So, if Khadija produces $ p $ phones, the variable cost would be $ 150p $.

The total cost $ C $ is the sum of the fixed cost and the variable cost. Hence, the equation will have the form:
\[
C = F + 150p
\]
We are also given that the total cost of producing 8 phones is $1800. Using this information, we can find $ F $ (the fixed cost). Substituting $ p = 8 $ and $ C = 1800 $ into the equation:
\[
1800 = F + 150(8)
\]
Simplifying:
\[
1800 = F + 1200
\]
\[
F = 1800 - 1200
\]
\[
F = 600
\]

Thus, the fixed cost $ F $ is $600. Now, substituting $ F = 600 $ into the general equation:
\[
C = 600 + 150p
\]

This is the equation for the total cost $ C $ in terms of the number of phones $ p $ produced in a day.

### Do you want further details or have any questions?
Here are 5 related questions to explore:

1. What would the total cost be if Khadija produces 15 phones in a day?
2. How many phones can Khadija produce if her total daily cost is $2550?
3. What is the fixed cost percentage in the total cost when producing 10 phones?
4. How does the cost function change if labor and material costs rise to $200 per phone?
5. If Khadija wants to minimize costs, how can she adjust her production schedule?

**Tip**: Fixed costs remain constant regardless of production quantity, but variable costs change with each additional unit produced.

Khadija is in the business of manufacturing phones. She must pay a daily fixed cost to rent the building and equipment, and also pays a cost per phone produced for materials and labor. The labor and materials cost $150 for each phone manufactured, and the total cost of producing 8 phones in a day would be $1800. Write an equation for C, in terms of p, representing total cost, in dollars, of producing p phones in a given day.

Learn how to calculate the total cost of manufacturing phones using a linear cost function. This example shows how to set up the equation C = 600 + 150p, where C is the total cost and p is the number of phones produced. Suitable for students in Grades 8-10.

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