TASK 1 – QUADRATIC FUNCTIONS The demand function for a new product is p(x) =-4x + 42.5, where x is the quantity sold in thousands and p is the price in thousands. The company that manufactures the product is planning to buy a new machine for the plant. There are three options they can choose from. The cost function for each machine is %3D shown below. Мachine A: C
TASK 1 – QUADRATIC FUNCTIONS The demand function for a new product is p(x) =-4x + 42.5, where x is the quantity sold in thousands and p is the price in thousands. The company that manufactures the product is planning to buy a new machine for the plant. There are three options they can choose from. The cost function for each machine is %3D shown below. Мachine A: C
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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![TASK 1- QUADRATIC FUNCTIONS
The demand function for a new product is p(x) =-4x + 42.5, where x is the
that
quantity sold in thousands and p is the price in thousands. The
manufactures the product is planning to buy a new machine for the plant. There
are three options they can choose from. The cost function for each machine is
соmрaпy
shown below.
Machine A: C(x) =-4.1x + 92.16
Machine B: C(«) ——17.9х + 29.36
Мachine C: C(x) — —8.9х + 55.4
1. Determine a revenue function given R(x) =x [p(x)] for Machine A. Show all your work.
[2K]
2. Determine a profit function given P(x) = R(x) – C(x) for Machine A. Show all your work.
-
[2K]
3. How many products, in thousands, does the company need to sell to break even; round your
answer(s) to the nearest whole number? Show all your work.
[4A, 1C]
4. Determine the maximum profit, in thousands, if the company chooses Machine A. Show all
your work.
[ЗА, 1C]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F5f87c213-2125-484a-abb9-131f346c9173%2Fa89528d7-2486-4520-8af2-cd9d41802894%2Frcj82em_processed.png&w=3840&q=75)
Transcribed Image Text:TASK 1- QUADRATIC FUNCTIONS
The demand function for a new product is p(x) =-4x + 42.5, where x is the
that
quantity sold in thousands and p is the price in thousands. The
manufactures the product is planning to buy a new machine for the plant. There
are three options they can choose from. The cost function for each machine is
соmрaпy
shown below.
Machine A: C(x) =-4.1x + 92.16
Machine B: C(«) ——17.9х + 29.36
Мachine C: C(x) — —8.9х + 55.4
1. Determine a revenue function given R(x) =x [p(x)] for Machine A. Show all your work.
[2K]
2. Determine a profit function given P(x) = R(x) – C(x) for Machine A. Show all your work.
-
[2K]
3. How many products, in thousands, does the company need to sell to break even; round your
answer(s) to the nearest whole number? Show all your work.
[4A, 1C]
4. Determine the maximum profit, in thousands, if the company chooses Machine A. Show all
your work.
[ЗА, 1C]
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