1. A small chemical company has estimated the price and the yearly volume produced of its top selling oxidizing agent. it's related by the following equation. 3000 V2 P - = Where P is the price per gallon of the oxidizing agent. The associated fixed costs are $4800 per year and the variable costs are $240 per gallon. Use this information to answer the following. a) Write out the full equation for the profit made from selling the oxidizing agent in terms of the volume. = Profit (3000 – V²) - 240 P-V3 +276V-4800 correct answer b) Determine the optimal volume of the oxidizing agent to be produced per year in gallons and obtain the maximum profit from the optimal volume. d(Profit) dv = a - Cv - 2BD = 0 show actual derivative c) The company's small capacity plant that produces the agent normally operates for a product rate of 30-60 gallons per year. Does the optimal demand from part (b) fall in this range or not? no, then will the plant have to reduce its capacity or increase it to maximize its profit? d) Find one of the break-even points from the profit equation. A value for volume, V that results in a profit value of 0. profit equation → p = bD² + (a c₁) D — Cf
1. A small chemical company has estimated the price and the yearly volume produced of its top selling oxidizing agent. it's related by the following equation. 3000 V2 P - = Where P is the price per gallon of the oxidizing agent. The associated fixed costs are $4800 per year and the variable costs are $240 per gallon. Use this information to answer the following. a) Write out the full equation for the profit made from selling the oxidizing agent in terms of the volume. = Profit (3000 – V²) - 240 P-V3 +276V-4800 correct answer b) Determine the optimal volume of the oxidizing agent to be produced per year in gallons and obtain the maximum profit from the optimal volume. d(Profit) dv = a - Cv - 2BD = 0 show actual derivative c) The company's small capacity plant that produces the agent normally operates for a product rate of 30-60 gallons per year. Does the optimal demand from part (b) fall in this range or not? no, then will the plant have to reduce its capacity or increase it to maximize its profit? d) Find one of the break-even points from the profit equation. A value for volume, V that results in a profit value of 0. profit equation → p = bD² + (a c₁) D — Cf
Practical Management Science
6th Edition
ISBN:9781337406659
Author:WINSTON, Wayne L.
Publisher:WINSTON, Wayne L.
Chapter2: Introduction To Spreadsheet Modeling
Section: Chapter Questions
Problem 20P: Julie James is opening a lemonade stand. She believes the fixed cost per week of running the stand...
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Transcribed Image Text:1. A small chemical company has estimated the price and the yearly volume produced
of its top selling oxidizing agent. it's related by the following equation.
3000 V2 P
_
Where P is the price per gallon of the oxidizing agent. The associated fixed costs are
$4800 per year and the variable costs are $240 per gallon. Use this information to
answer the following.
a) Write out the full equation for the profit made from selling the oxidizing agent in
terms of the volume.
=
Profit (3000 - V²) - 240
P = -V³ +276V-4800 → correct answer
b) Determine the optimal volume of the oxidizing agent to be produced per year in
gallons and obtain the maximum profit from the optimal volume.
d(Profit)
dv
= a - Cv
-
2BD = 0
show actual derivative
c) The company's small capacity plant that produces the agent normally operates
for a product rate of 30-60 gallons per year. Does the optimal demand from part
(b) fall in this range or not? no, then will the plant have to reduce its capacity or
increase it to maximize its profit?
d) Find one of the break-even points from the profit equation. A value for volume, V
that results in a profit value of 0.
profit equation → p = bD² + (a − cv)D — Cf
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