# Thread: optimization question

1. ## optimization question

Hello

I have a function that represents the amount of objects sold S(x)=-15.4x+3633 and a function that is used to calculate profit from sales P(x)= S*x
Problem is to calculate at what price does the company get the most profit, so my solution is to make a function of profit(P) as function of price(x) and it comes out as P(x)=x(-15.4x+3633), then derive it, set the derivative to 0 and look for max. I get an answer of 118 currency. Does it look right? Thanks

S= units sold
x= Price

2. ## Re: optimization question Originally Posted by dbag Hello

I have a function that represents the amount of objects sold S(x)=-15.4x+3633 and a function that is used to calculate profit from sales P(x)= S*x
Problem is to calculate at what price does the company get the most profit, so my solution is to make a function of profit(P) as function of price(x) and it comes out as P(x)=x(-15.4x+3633), then derive it, set the derivative to 0 and look for max. I get an answer of 118 currency. Does it look right? Thanks

S= units sold
x= Price
It doesn't need to LOOK right, it needs to BE right.
Did you create the proper Profit Function?
Did you find the proper derivative?
Did you make any errors solving for the desired value?
Did you check the 2nd derivative at your solution point (or use some other method) to make sure it was a maximum?
Were you instructed to round to Whole "currency"?

Answer all the questions and you can know for yourself whether your work is up to speed.

3. ## Re: optimization question

Is the profit function right? I dont know
The 1st derivative would be -30.8x and then finding the max point it would come out to 30.8x=3633 --> x=117.95
2nd derivative would be -30.8
no rounding required.

4. ## Re: optimization question Originally Posted by dbag Is the profit function right? I dont know
The 1st derivative would be -30.8x + 3633 and then finding the max point it would come out to 30.8x=3633 --> x=117.95
2nd derivative would be -30.8
no rounding required.
see red above

Usually:
Qty Sold x Price each = REVENUE
and
PROFIT = Revenue - Cost

Only if there is no cost (unlikely) will revenue and profit be the same.

Were you given information about the cost of producing the product (different to the price at which it is sold)?
Or were you asked to maximise revenue?

It'd be helpful if you posted the entire original question.

5. ## Re: optimization question

Original question: A product is sold at 4 different prices and the demand has been higher when price is lower. At 178 currency product was sold 859 times. At price 169 its was sold 1112 times. 189 currency… sold 701 times and at 160 currency it was sold 1109 times. According to these stats we get a function that represents the amount of units sold and it goes like this Product sold= -15.4*price+3633. The profit from sales is then calculated by multiplying the amount of products sold by their price and that is Profit=Products sold*price. The problem asks to optimize at what price/product do we maximize profit.

6. ## Re: optimization question Originally Posted by dbag Is the profit function right? I dont know
The 1st derivative would be -30.8x and then finding the max point it would come out to 30.8x=3633 --> x=117.95
2nd derivative would be -30.8
no rounding required.
How do you not know? (Profit / Unit) * Units = Profit. ==> S(x) * x = P(x) = profit function. You CAN KNOW that it is correct. Did you do it wrong deliberately?

If P(x) = x (-15.4x+3633 ) = -15.4x^2 + 3633x, P'(x) = -30.4x + 3633 -- That is not what you said, but it is what you meant. Be much more careful with your notation and you will see more clearly.

Your original answer was x = 118. That is rounded. You just decided to round. No need for that. Do it only when required to do so. In this case, rounding may be appropriate. Maybe you can't sell partial units. In that case, it would be better to test x = 117 and x = 118, rather than just assume that some sort of rounding will achieve the maximum.

Good work. You seem to have the right idea.

7. ## Re: optimization question

Thank you very much