Question

Minimize the following cost function ; TC = 1/3q^3 - 8 . 5q^2 + 60q+27

Minimize the following cost function ; TC = 1/3q^3 - 8 . 5q^2 + 60q+27

Business   Economics   
0 0
Add a commentTranscribed image text
Next >

Homework Answers

Answer #1

TC = q3/3  - 8 .5q2 + 60q + 27  

dTC/dq = 3q2/3 - 17q + 60  

= q2 - 17q + 60  

put dTC/dq = 0  

q2 - 17q + 60 = 0  

q2 - 5q - 12q + 60 = 0  

q(q - 5) -12(q - 5) = 0  

(q - 12)(q - 5) = 0  

q - 12 = 0 or q - 5 = 0

q = 12 or q = 5

SOC  

d2TC/dq2 = 2q - 17  

at q = 5  

d2TC/dq2 = 2(5) - 17 = 10 - 17 = - 7

d2TC/dq2 < 0

Therefore cost is maximum at q = 5

at q = 12  

d2TC/dq2 = 2(12) - 17 = 24 - 17 = 7

d2TC/dq2 > 0  

so cost is minimum at q = 12

Minimumm TC = (123)/3 - 8.5(12)2 + 60(12) + 27  

= 576 - 1224 + 720 + 27

= 1323 - 1224

= 99

0 0
Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Log In

Sign Up

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
A firm's total cost function is given by the equation: TC = 4000 + 5Q +...
A firm's total cost function is given by the equation: TC = 4000 + 5Q + 10Q2. (1) Write an expression for each of the following cost concepts: a. Total Fixed Cost b. Average Fixed Cost c. Total Variable Cost d. Average Variable Cost e. Average Total Cost f. Marginal Cost (2) Determine the quantity that minimizes average total cost and minimizing average variable cost. (3) Why does its average variable cost curve achieve its minimum at a lower level...
For the following total-revenue and total-cost functions of a firm: TR= 22Q - 0.5Q^2 TC= 1/3Q^3...
For the following total-revenue and total-cost functions of a firm: TR= 22Q - 0.5Q^2 TC= 1/3Q^3 - 8.5Q^2 + 50Q + 90 a.) determine the level of output at which the firm maximizes its total profit. b.) determine the maximum profit the firm could earn ** please explain step by step. I am very confused as to work this problem.
Consider two firms with the cost function TC(q) = 5q (constant average and marginal cost,of 5),...
Consider two firms with the cost function TC(q) = 5q (constant average and marginal cost,of 5), facing the market demand curve Q = 53 – p (where Q is the total of the firms’ quantities, and p is market price). a. What will be each firm’s output and profit if they make their quantity choices simultaneously (as Cournot duopolists)? b. Now suppose Firm 1 is the Stackelberg leader (its decision is observed by Firm 2 prior to that firm’s decision)....
TC=8,000+3Q+0.004Q2 so its marginal cost is thus MC=3+0.008Q
TC=8,000+3Q+0.004Q2 so its marginal cost is thus MC=3+0.008Q
Consider the cost function C= 40 + 3Q 2Q^2 + 1/2Q^3 . i) At Q =...
Consider the cost function C= 40 + 3Q 2Q^2 + 1/2Q^3 . i) At Q = 4, what is the firm’s average fixed cost? ii) At Q = 4, what is the firm’s marginal cost? iii) If the firm optimally produces Q = 4, and P = 35-aQ, what does a have to be? iv) Which Q minimizes the firm’s average variable cost? v) What is the firm’s minimum average variable cost?99
Suppose the demand model and the cost function facing a firm is expressed as P= 120-5Q...
Suppose the demand model and the cost function facing a firm is expressed as P= 120-5Q and TC= 20+ 30Q + 2Q2 1. Calculate i.                 the profit maximizing equilibrium level of output that the monopolist will produce ii.               the price that the monopolist would charge iii.             and the profit of the monopolist
The total cost function for a firm in a perfectly competitive market is TC = 350...
The total cost function for a firm in a perfectly competitive market is TC = 350 + 15q + 5q2. At its profit maximizing quantity in the short-run, each firm is making a loss but chooses to stay open. Which of the following is/are necessarily true at the profit maximizing quantity? MR = 15 + 5q P>15 AR > 350/q + 15 + 5q Both A and B are true. Both B and C are true. All of the above...
Consider a competitive industry with firms that have these cost functions: TC = q^3 - 8...
Consider a competitive industry with firms that have these cost functions: TC = q^3 - 8 q^2 + 24 q   AC = q^2 - 8 q + 24 =   (q-4)2 + 8       MC = 3q^2 - 16 q + 24           In the short run, if P = 30, a.   What q will the firm produce? (Feel free to round off but show your work.) b.   What π (profit) will the firm make? (Feel free to round off...
You are given the following total cost function for a firm:            TC = (25+F) + L...
You are given the following total cost function for a firm:            TC = (25+F) + L x Q + 0.5 x (Q2) where F=the number of the letter of the alphabet corresponding to the initial of your first name, and L=number of the letter of the alphabet corresponding to the initial of your last name.  For example, if your name were Bill Weber, F=2 and L=23, so TC = 27 + 23 x Q + 0.5 x Q2. a.         Calculate TC, TFC,...
Consider a firm with a short run Total Cost (TC) given by TC=200 + 30Q -...
Consider a firm with a short run Total Cost (TC) given by TC=200 + 30Q - 5Q^2 + Q^3. What is the firm’s fixed cost? What is the firm’s marginal cost? What is firm's shut down price?
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT