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.

1. Given the following total cost function of C (q) = 400Q(squared) - 20Q + 7
Calculate Averagecost,Marginalcost,Average Variable Costand the output level at which Average Variable Cost is at a minimum.

The total cost of producing Q units of a commodity is:
C(Q) = 4Q^2 + 40Q + 36 Q > 0
Show that the Q that minimizes the averagecost A(Q) also is the Q where the marginalcost is equal to the averagecost.

The cost function for a business is shown in the table below (where Q is the level of output):
Q (units) Cost
0 8
1 24
2 38
3 44
4 51
5 52
6 59
7 65
8 79
9 95
10 125
Calculate the (a) marginalcostand (b) the average total cost schedules.

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

The market demand function of a firm is given by 8P + Q - 64 = 0, and the firm's averagecost function takes the form AC = 8/Q + 6 - 0.4Q + 0.08Q2.
i)Determine the price and quantity for maximum sales revenue and calculate the maximum revenue.
ii)Determine the price and quantity for minimummarginalcosts and calculate the min

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