Word Problems

[jillpil87]

I've always hated these. Perhaps you can be of some help?!

The price p and the quantity x sold of a certain product obey the demand equation
x= -5p+100, 0<x<300

a) express the revenue R as a function of x.
b) what quantity x maximizes revenue? What is the maximum revenue?
c) what price should the company charge to maximize revenue?



A farmer with 4000 meters of fencing wants to enclose a rectangular plot that borders on a river. If the farmer does not fence the side along the river, what is the largest area that can be enclosed?


Thanks for any help you can give!

 

[skeeter]

I've always hated these. Perhaps you can be of some help?!

The price p and the quantity x sold of a certain product obey the demand equation
x= -5p+100, 0<x<300

a) express the revenue R as a function of x.
revenue = (price)(quantity sold) ...
R = p(x) = p(-5p+100)
b) what quantity x maximizes revenue? What is the maximum revenue?
hint ... max R will occur at the vertex of the parabola formed by the revenue equation in part (a)
c) what price should the company charge to maximize revenue?
ditto the hint given for part (b)

A farmer with 4000 meters of fencing wants to enclose a rectangular plot that borders on a river. If the farmer does not fence the side along the river, what is the largest area that can be enclosed?
let x = single length parallel to the river
y = two lengths needed perpendicular to the river
x + 2y = 4000
area, A = xy = (4000 - 2y)y
hint ... note that the graph of the area function is an inverted parabola ... where is the vertex?


Thanks for any help you can give!