Question

If C(x) is the cost of producing x units of a commodity, then the average cost per unit is a(x) = C(x)/x. Consider the C(x) given below. Round your answers to the nearest cent. C(x) = 2,000 + 140x + 4x^3/2 Find the total cost at a production level of 1000 units.

Answer 1

At a production level of 1000 units, the total cost Cₓ₊₁₀₀₀ is approximately $142,900.

Step-by-step explanation:

To find the total cost at a production level of 1000 units, substitute x = 1000 into the cost function Cₓ = 2,000 + 140x + (4x^(3/2))/2:

Cₓ₊₁₀₀₀ = 2,000 + 140 * 1000 + (4 * 1000^(3/2))/2

Cₓ₊₁₀₀₀ = 2,000 + 140,000 + (4 * 1000^(3/2))/2

Cₓ₊₁₀₀₀ = 2,000 + 140,000 + 4 * 500

Cₓ₊₁₀₀₀ = 2,000 + 140,000 + 2,000

Cₓ₊₁₀₀₀ = 142,000 + 2,000

Cₓ₊₁₀₀₀ = 144,000

Therefore, the total cost at a production level of 1000 units is $144,000.

Understanding the total cost at a given production level is essential for effective cost management and budgeting. In this scenario, the cost function Cₓ accounts for fixed costs, variable costs, and costs associated with production quantity. The evaluation of Cₓ₊₁₀₀₀ provides the total cost at the specified production level, aiding businesses in making informed decisions regarding production quantities and associated costs.