Derivatives : Average Cost, Marginal Cost and Minimum Cost

If it costs Acme Manufacturing C dollars per hour to operate its golf ball division, and an analyst has determined that C is related to the number of golf balls produced per hour, x, by the equation C = 0.009x squared - 1.8x + 100. What number of balls per hour should Acme produce to minimize the cost per hour of manufacturing these golf balls?

Solution Preview

C = 0.009x^2 - 1.8x + 100
The first order condition to minimize the cost is:
marginal cost = average ...

Solution Summary

Derivatives are used to find minimum cost. The solution is detailed and well presented. The response received a rating of "5" from the student who originally posted the question.

Complete the following table. What is the value of fixed cost?
Output Total CostMarginalCostAverageCost
0 $100
1 $110
2 $130
3 $165
4 $220
5 $300
On a graph, depict marginalcostandaveragecost using the data from above. Indicate minimumaveragecost on the graph.

Given the following table:
Complete the following table (round each answer to the nearest whole number):
Total Variable Fixed MarginalAverage Avg. Var. Avg. Fixed
Output CostCostCostCostCostCostCost
0
1 5
2 30
3 13
4 105 10
5 110
6 50
Complete the table then

The Dijon Company's total variable cost function is:
TVC = 50Q -10Q^2 + Q^3
where Q is the number of units of output produced.
a. What is the output level where marginalcost is at minimum?
b. What is output level where average variable cost is a minimum?
c. What is the value of average va

Construct line charts for the AverageCost (AC), Average Variable Cost (AVC), MarginalCost (MC), Marginal Revenue (MR) andAverage Revenue (AR) on a Cartesian coordinate system.

Explain how each of the following will affect the average fixed cost,average variable cost,average total cost,andmarginalcost curves faced by a steel manufacturer:
1. New union agreement increases hourly pay.
2. Local government imposes an annual lump-sum tax per plant.
3. Federal government imposes a "s

(i) Suppose a firm's short-run averagecost curve is U shaped: what does this imply about the marginal return to the variable input? (ii) Comment on the following statement: "Averagecost includes both fixed and variable costs, whereas marginalcost only includes variable costs. Therefore, marginalcost is never greater than ave

A manufacturer of small chain saws has determined:
R(x)=xp(x)=x(200-x/30)=200x-x^2/30
C(x)=7200+60x
Where x is the number of saws that can be sold at price $p per saw and C(x) is the total cost (in dollars) of producing x saws.
a. Find the marginalcost
b. Find the marginal revenue
c. What is the minimum number of saws s

1. If the government imposes a $1 per-unit tax, how do the marginal, average total, andaverage variable costs change? What if instead the government imposes a $100 per-firm tax?
2. a) Why are short-run marginalcost curves expected to slope upward?
b) If you know that averagecosts are increasing, is the marginalcost

A) If the government imposes a $1 per-unit tax, how do the marginal, average total, andaverage variable costs change? What if instead the government imposes a $100 per-firm tax? (ASSUME NO CHANGE IN THE AMOUNT OF SALES.)
B) Why are short-run marginalcost curves expected to slope upward?
C) If you know that averagecost