SOLUTION: A South African country exports gold and estimates the demand function to be D(p)=400√2600-p. If the country wants to raise revenues to improve the balance of payments, shou

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Question 900809: A South African country exports gold and estimates the demand function to be D(p)=400√2600-p. If the country wants to raise revenues to improve the balance of payments, should it raise or lower the price from the present level of $1600 per ounce?
Little help please. I have always struggled with word problems.
Answer by MathTherapy(10551) About Me  (Show Source):
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A South African country exports gold and estimates the demand function to be D(p)=400√2600-p. If the country wants to raise revenues to improve the balance of payments, should it raise or lower the price from the present level of $1600 per ounce?
Little help please. I have always struggled with word problems.


highlight%28D%28p%29+=+400sqrt%282600+-+p%29%29



Based on the demand equation/function, and a price of $1,600, per oz, the demand for gold would be:

highlight_green%28highlight_green%2812649.11%29%29 oz, with revenues of approximately $Mhighlight_green%28highlight_green%2820.24%29%29. 



Based on the demand equation/function, and a $100, per oz price INCREASE, to $1,700, per oz, the demand

for gold would be: highlight_green%28highlight_green%2812000%29%29 oz, with revenues of $Mhighlight_green%28highlight_green%2820.4%29%29



Based on the demand equation/function, and a $100, per oz price REDUCTION, to $1,500, per oz, the demand

for gold would be: highlight_green%28highlight_green%2813266.49916%29%29 oz, with revenues of approximately $Mhighlight_green%28highlight_green%2819.9%29%29. 



It is quite obvious that in this situation, and most similar ones, the cheaper the price, the higher the demand.

However, in this case, an INCREASE in price, which leads to a lower demand would DEFINITELY garner higher revenues.

Thus, the price should be INCREASED.