We are given the following details:

• The development cost is a fixed cost of $5200.
• Each toy costs $10 to manufacture.
• $n$ represents the number of toys produced.

A.) Linear equation for total cost

The total cost $C$ includes the fixed cost of $5200 and the variable cost of $10 per toy. Thus, the linear equation in the form $C = mn + b$ is:

$C = 10n + 5200$

B.) Total cost to produce 1350 toys

Substitute $n = 1350$ into the equation $C = 10n + 5200$:

$C = 10(1350) + 5200 = 13500 + 5200 = 18700$

So, the total cost to produce 1350 toys is $18,700.

C.) Number of toys that can be produced with $36,700

We are given that the total cost is $36,700. Use the equation $C = 10n + 5200$, and set $C = 36700$:

$36700 = 10n + 5200$

Solve for $n$:

$36700 - 5200 = 10n$ $31500 = 10n$ $n = \frac{31500}{10} = 3150$

So, 3150 toys can be produced with $36,700.

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

1. What if the fixed cost increased to $6000? How would the equation change?
2. How would the cost equation change if it costs $12 to manufacture each toy?
3. How many toys can be produced with $50,000?
4. If 500 toys were produced, what would the total cost be?
5. How does the number of toys produced affect the total cost?

Tip: When working with linear cost functions, the fixed cost is the y-intercept, and the per-unit cost is the slope.