1. Dr. Poage has decided to produce and sell rings that say "V-1 ♡ MATH!" The price-demand equation and cost function to produce these rings are given respectively by: C(x)= 72000+ 60x, where x is the number of rings that can be sold at a price of $p per Souns von mumizan od ei elw (e p=-+200 p=-30+ %3D ring and C(x) is the total cost (in dollars) of producing x rings. (a) Determine the break-even point(s). lloa A gaubonq ogos bas borl taum ebnuw am woH (bruw on of bnuon) So nond (b) What is the maximum Revenue? Box fal Sebrow peodt no alam bluos vodi tdoq munixem orli al ted W (c) How many rings are needed to maximize the Revenue?

Advanced Engineering Mathematics
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ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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How do I solve parts A-H for the following problem?
**Problem Statement:**

Dr. Poage has decided to produce and sell rings that say “√−1 ❤ MATH!” The price-demand equation and cost function to produce these rings are given respectively by:

\[ p = -\frac{x}{30} + 200 \]
\[ C(x) = 72000 + 60x \]

where \( x \) is the number of rings that can be sold at a price of \( p \) per ring and \( C(x) \) is the total cost (in dollars) of producing \( x \) rings.

**Questions:**

(a) Determine the break-even point(s).

(b) What is the maximum Revenue?

(c) How many rings are needed to maximize the Revenue?

(d) What should the rings be priced at to maximize the Revenue?

(e) Find the Profit function and simplify.

(f) How many rings are needed to maximize the Profit?

(g) What is the maximum profit?

(h) What should the rings be priced at to maximize the profit?
Transcribed Image Text:**Problem Statement:** Dr. Poage has decided to produce and sell rings that say “√−1 ❤ MATH!” The price-demand equation and cost function to produce these rings are given respectively by: \[ p = -\frac{x}{30} + 200 \] \[ C(x) = 72000 + 60x \] where \( x \) is the number of rings that can be sold at a price of \( p \) per ring and \( C(x) \) is the total cost (in dollars) of producing \( x \) rings. **Questions:** (a) Determine the break-even point(s). (b) What is the maximum Revenue? (c) How many rings are needed to maximize the Revenue? (d) What should the rings be priced at to maximize the Revenue? (e) Find the Profit function and simplify. (f) How many rings are needed to maximize the Profit? (g) What is the maximum profit? (h) What should the rings be priced at to maximize the profit?
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