Final answer:
The cost function formula T C(q) = 400 + 5q + 10q² is used to calculate different costs such as total cost (TC), fixed cost (FC), variable cost (VC), and average total cost (ATC) for different quantities produced.
Step-by-step explanation:
The total cost (TC) can be calculated by adding the fixed cost (FC) and variable cost (VC). In this case, the fixed cost is $400 and the variable cost is given by the formula 5q + 10q², where q is the quantity produced. To calculate the total cost for different quantities produced, substitute the values of q in the cost function. For q = 5, the total cost is 400 + 5(5) + 10(5)² = $675. For q = 10, the total cost is 400 + 5(10) + 10(10)² = $1,500. And for q = 15, the total cost is 400 + 5(15) + 10(15)² = $2,725.
The fixed cost (FC) is the cost that does not vary with the quantity produced. In this case, the fixed cost is $400.
The variable cost (VC) is the cost that varies with the quantity produced. In this case, the variable cost is given by the formula 5q + 10q², where q is the quantity produced. To calculate the variable cost for different quantities produced, substitute the values of q in the cost function. For q = 5, the variable cost is 5(5) + 10(5)² = $275. For q = 10, the variable cost is 5(10) + 10(10)² = $1,000. And for q = 15, the variable cost is 5(15) + 10(15)² = $2,325.
The average total cost (ATC) is calculated by dividing the total cost by the quantity produced. For q = 5, the average total cost is 675/5 = $135. For q = 10, the average total cost is 1500/10 = $150. And for q = 15, the average total cost is 2725/15 = $181.67.