P= 10,000-2Q C = 16,000+ 1648Q +0.4Q² a. Determine the quantity (Q) that maximizes profit. b. Calculate P, R, C, AC, and at the optimal quantity found in part a. c. Determine the quantity (Q) that maximizes total revenue. d. Calculate P, R, C, AC, and at the optimal quantity found in part c. e. Determine the quantity (Q) that minimizes average cost. f. Calculate P, R, C, AC, and x at the optimal quantity found in part e. Equations: Rules for Optimization Profit Maximization MR = MC Revenue Maximization MR 0 Average Cost Minimization MC = AC or Shortcut: for C= a +bQ+cQ² II=R-C R =P* Q AC = C/O Q = (a/c)1/2
P= 10,000-2Q C = 16,000+ 1648Q +0.4Q² a. Determine the quantity (Q) that maximizes profit. b. Calculate P, R, C, AC, and at the optimal quantity found in part a. c. Determine the quantity (Q) that maximizes total revenue. d. Calculate P, R, C, AC, and at the optimal quantity found in part c. e. Determine the quantity (Q) that minimizes average cost. f. Calculate P, R, C, AC, and x at the optimal quantity found in part e. Equations: Rules for Optimization Profit Maximization MR = MC Revenue Maximization MR 0 Average Cost Minimization MC = AC or Shortcut: for C= a +bQ+cQ² II=R-C R =P* Q AC = C/O Q = (a/c)1/2
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter7: Analytic Trigonometry
Section7.6: The Inverse Trigonometric Functions
Problem 94E
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Transcribed Image Text:P=10,000-2Q
C = 16,000+ 1648Q +0.4Q²
a. Determine the quantity (Q) that maximizes profit.
b. Calculate P, R, C, AC, and at the optimal quantity found in part a.
c. Determine the quantity (Q) that maximizes total revenue.
d. Calculate P, R, C, AC, and at the optimal quantity found in part c.
e. Determine the quantity (Q) that minimizes average cost.
f. Calculate P, R, C, AC, and at the optimal quantity found in part e.
Equations:
Rules for Optimization
Profit Maximization
MR = MC
Revenue Maximization
MR=0
Average Cost Minimization
MC = AC or
Shortcut: for C= a +bQ+cQ²
II=R-C
R =P* Q
AC = C/O
Q = (a/c)1/2
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