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Did I miss something? The problem is below. I don't care about the final answer, just need help fixing any steps.

Price (p) and quantity (q) share the relationship- p=-.006x+1800

Determine Revenue function, R(x) for selling x units. I have R(x)= # of units*price per unit or R(x)=x*p so R(x)=x(-0.006x+1800)=-0.006x^2+1800x Correct?

Derive a profit function P(x) if cost of prduction is known as C(x)=12,100,000+800x+0.04x^2. I have Profit = Revenue- Cost or P(x)=R(x)-C(x). So P(x)=(-0.006x^2+1800x)-(12,100,000+800x+0.04x^2)= -0.006x^2+1800x-12,100,000-800x-0.04x^2 =-0.046x^2+1000x-12,100,000. Correct?

How many units should be made for max profit? What is the max profit?

For # of units, Max of x is needed. I used the derivitive of P(x) for this as P'(x)=-.092x+100. Set it to 0 so that x=1000/.092 units. Double prime>0 so it's a max. Correct?

Max profit- P(1000/.092)=-.046(1000/.092)^2+1000(1000/.092)-12,100,000 =-66,652,217.40

Is that really right? Neg. profit?

2007-04-03 20:33:45 · 4 answers · asked by Anonymous in Science & Mathematics Mathematics

4 answers

Of course. happens all the time in business. So you can go tell your boss not to do the project or whatever.

I checked your calculations, they're correct. Think of it like this: what's the max revenue? the max of that function is at the zero of its derivative, at
x = 1800/.012 = 150000 units.

that produces a total revenue of 135000. Now check what the cost of producing 150000 units is:
1, 032, 100, 100.

and of course for zero units revenue is zero and cost is 12,100,000.

What you did was simply show that there is no point x between 0 and 150000 for which revenue exceeds cost.

Drop the venture, or keep the numbers from the stockholders.


btw you did make one error only: you said the double-prime >0 indicates a max, actually double-prime < 0 indicates a max, but since the double prime was the constant -.006 (negative) that made no difference.

2007-04-03 21:35:44 · answer #1 · answered by kozzm0 7 · 0 0

Yes, that is right. I tried calculating it and I got a negative profit too. It goes like this:
x = 1000/0.092 = 10,870 units
p(10,870) = ~65 (price per unit)
R(10,870) = 10870*65 = 708,913
So you have a revenue of about 700 000, and fix costs of over 12 millions. Add the variable costs and you get those million losses.
The maximum doesn't necessary mean that there is positive profit. At this point, the company will made the least loss, that's why it is a maximum. In reality, with such a cost structure and demand curve, you just don't get any suppliers. and the market for this good doesn't exist.

2007-04-03 20:57:39 · answer #2 · answered by Rumtscho 3 · 0 0

your steps are correct.
your calculations might be wrong.
since profit is maximised at whatever value you got, the profit cannot be ngeative.(since a maximum profit being loss is not good for any business.)

check your calculations.

2007-04-03 20:46:41 · answer #3 · answered by Titan 4 · 0 0

Your mother!!!!

2007-04-03 20:35:42 · answer #4 · answered by cflip5 1 · 0 1

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