Somebody please help about my Math question.(Urgent)

[dark80809]

I have tried to do this questions but i still can't solve this question. Please help me. Thanks.

The demand function for a good is P = - 0.25Q + 500

(a) Write down the equation for the total revenue function.
(b) Sketch the graph of the total revenue function.
(c) Determine the maximum total revenue.

[Guest]

I notice you have "tried" this question...??
Where is your reasoning............???
It is a linear type function...y = mx + c

Post some working and we can help point you in the right direction

[dark80809]

I notice you have "tried" this question...??
Where is your reasoning............???
It is a linear type function...y = mx + c

Post some working and we can help point you in the right direction

sP = -0.25Q + 500
a) total revenue = Q(-0.25Q + 500)
-0.25Q^2+ 500Q

Answer -0.25Q^2+ 500Q

b) I don't know how to sketch.

c) Maximum Revenue is where Q= 500 / -2(-0.25)
Q= 500 / 0.50
Q = 1000
Going back to the revenue function -0.25Q^2+ 500Q
Substitute 1000 for Q
Max total revenue = -0.25(1000)^2 + 500(1000)
= - 250,000+ 500,000
= 250,000

Is these correct? I'm not sure about it. Idk how to sketch it out. Can u help me on that too ?

[Guest]

Yes, the equation for Total Revenue will be P x Q which you have worked out ok.

The demand function graph is.............
The graph would be plotted with P vertical in the Y axis and Q horizontal on the X axis
The demand function is linear so will be a straight line with a -ve slope -f -0.25 and crossing the Y axis at +500.
It will also cross the X axis when P=0 that is when 0.25Q = 500 that is when when Q = 2000

The Total Revenue Function graph...........
Total Revenue = TR = P x Q = -0.25Q^2 + 500Q
This is a quadratic function with a =ve coefficient of Q so will be an upsidedown parabola
This can be drawn by making a table for various values of P and Q that satisfy the revenue equation, and plot on graph paper.
The maximum of this function will be at the top of the curve when the slope is Zero. So you can find this point from the graph or differentiate the function and put it equal to Zero and solve for Q.

So.....dTR/dQ = -2 x 0.25Q + 500 = 0 then.... 0.5Q = 500 So Q = 1000 when curve/function is at maximum.

You are asked to sketch the curve, so that means sketch it don't need to make table for accurate plot.
From the info so far for sketching....The curve is -ve parabola upside down curve, Max of curve at top where it bends to come down again, this is when Q = 1000. It will cross the X axis at Q=0, P=0, because there is no constant term. It will be symmetrical about the vertical line Q=1000 so crosses the X axis at Q=2000.

Part (c) you have worked out the total maximum revenue ok.

................Simple.................................

[Guest]

Sorry error again........
Tis line in above post...........
It will cross the X axis at Q=0, P=0, because there is no constant term.

Should read.................
It will cross the X axis at Q=0, TR=0, because there is no constant term.