ASKSAGE: Sage Q&A Forum - RSS feedhttps://ask.sagemath.org/questions/Q&A Forum for SageenCopyright Sage, 2010. Some rights reserved under creative commons license.Sun, 10 Oct 2021 23:10:33 +0200Solving equationhttps://ask.sagemath.org/question/59316/solving-equation/ To encourage buyers to place 100-unit orders, your firm’s sales department applies a continuous discount that makes the unit price as a function P(x) of the number of unites ordered. The discount decreases the prices at the rate EUR 0.01 per unit ordered. The price per unit for a 100-unit order is P(100) = 20.09 EUR.
(a) Find P(x) by solving the equation
P′(x) = − 1/100 P(x), P(100) = 20.09.
(b) Find the unit price P(10) for a 10-unit order and P(90) for a 90-unit order.
(c) The sales department has asked you to find out if it is discounting so much that the firm’s revenue, r(x) = xP(x), will actually be less for a 100-unit order than, say, for a 90-unit order. Reassure them by showing that r(x) has its maximum value at x = 100.
(d) Graph the revenue function r(x) = xP(x) for 0 ≤ x ≤ 200.Sun, 10 Oct 2021 16:42:46 +0200https://ask.sagemath.org/question/59316/solving-equation/Comment by tmonteil for <p>To encourage buyers to place 100-unit orders, your firm’s sales department applies a continuous discount that makes the unit price as a function P(x) of the number of unites ordered. The discount decreases the prices at the rate EUR 0.01 per unit ordered. The price per unit for a 100-unit order is P(100) = 20.09 EUR.
(a) Find P(x) by solving the equation
P′(x) = − 1/100 P(x), P(100) = 20.09.</p>
<p>(b) Find the unit price P(10) for a 10-unit order and P(90) for a 90-unit order.</p>
<p>(c) The sales department has asked you to find out if it is discounting so much that the firm’s revenue, r(x) = xP(x), will actually be less for a 100-unit order than, say, for a 90-unit order. Reassure them by showing that r(x) has its maximum value at x = 100.</p>
<p>(d) Graph the revenue function r(x) = xP(x) for 0 ≤ x ≤ 200.</p>
https://ask.sagemath.org/question/59316/solving-equation/?comment=59320#post-id-59320This looks like homework.
If you want some help, you should ask more precise questions related to your research in solving those exercises, especially where you are locked.Sun, 10 Oct 2021 23:10:33 +0200https://ask.sagemath.org/question/59316/solving-equation/?comment=59320#post-id-59320