Optimum production level of chocolate bar with a weight of 100g.

yhpigs

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Aug 12, 2018
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Hello! I'm here yet again with another question *sigh*.

I'll write the background info here:
A chocolate factory will sell a new chocolate bar with a weight of 100g.
They will sell for $2.00 each and 300 000 will be sold each week. For every price rise of 10c, sales will drop by 5 100 bars per week.
Manufacturing cost is 50c/100g of chocolate, + 0.213 cents/cm^2 for the wrapping.
The shape of the chocolate bar is an equilateral triangular prism.

I've already found the revenue from the weekly sales of the chocolate bars:

Screen Shot 2018-08-19 at 10.05.01 pm.jpg

Screen Shot 2018-08-19 at 10.06.00 pm.jpg


Now I need to determine the number of chocolate bars to be manufactured per week which will maximise revenue, but I've only managed to find the manufacturing cost so far, which is:
0.5 + 0.213 * SA (surface area) [note: SA = 21.84cm^2]
= 0.713x * 21.84

Not sure what to do from here. Thanks in advance for any help!
 
They will sell for $2.00 each and 300 000 will be sold each week. For every price rise of 10c, sales will drop by 5 100 bars per week.
Manufacturing cost is 50c/100g of chocolate, + 0.213 cents/cm^2 for the wrapping.
The shape of the chocolate bar is an equilateral triangular prism.

I've already found the revenue from the weekly sales of the chocolate bars:

View attachment 9977

View attachment 9978


Now I need to determine the number of chocolate bars to be manufactured per week which will maximise revenue, but I've only managed to find the manufacturing cost so far, which is:
0.5 + 0.213 * SA (surface area) [note: SA = 21.84cm^2]
= 0.713x * 21.84
From what you've posted, you've already determined the maximising info for the revenue, by finding R', etc. Are you maybe supposed to find the conditions which will maximise the "profit"...? Because this would allow you to bring the costs into play, since profits are revenues less expenses.

If so, then I'd start by coming up with a "cost" equation, subtracting this from the "revenue" equation, and then differentiating the resulting "profit" equation. (I can't see any need for doing anything with R'.) ;)
 
From what you've posted, you've already determined the maximising info for the revenue, by finding R', etc.

Thank you! I hadn't realised this. :D So would the value I've found from R' be the number of products that need to be made per week?
 
Thank you! I hadn't realised this. :D So would the value I've found from R' be the number of products that need to be made per week?
Since you're trying to maximize profit, not revenue, I'm saying that the value you've found from R' is irrelevant. Instead, try working with the "profit" formula.
 
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