Pace's total cost of producing CO₂ cartridges is given by TC = 0.5X ³ - 24X ² + 144X.The level of output that minimizes average total cost is: A) 12 cartridges. B) 10 cartridges. C) 18 cartridges. D) 20 cartridges. E) 24 cartridges.

Question

Quizplus · Accepted Answer

To minimize the average total cost (ATC), we first need to find the derivative of the total cost (TC) function and then set it equal to zero to solve for X. The total cost function given is TC = 0.5X^3 - 24X^2 + 144X. The average total cost (ATC) is TC/X, but to find the minimum ATC, it's more straightforward to work with the marginal cost (MC), which is the derivative of TC with respect to X. The derivative of TC is d(TC)/dX = 1.5X^2 - 48X + 144. Setting this equal to zero and solving for X gives the level of output that minimizes the ATC. Solving 1.5X^2 - 48X + 144 = 0 gives X = 24 as one of the solutions, which corresponds to the minimum ATC.

Pace's Total Cost of Producing CO2 Cartridges Is Given by TC

Pace's Total Cost of Producing CO₂ Cartridges Is Given by TC