Economics Math Problem Assignment: Maximizing Revenue (Math Problem Sample)

Maximizing Revenue
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November 25th, 2016
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Maximizing Revenue
Given that revenue is represented by the function R (p) = – 0.5p2 + 1900p, we first seek to calculate the price that should be charged so as to enable John Deere to obtain maximum revenue. This price (p) is given by,
Price= -b/2a
= -1900/2(-0.5)
Unit price (P) = 1900
Once the price for every unit (p) has been calculated. We seek to find the maximum revenue that John Deere will be raising at the price obtained above. This is calculated by,
Revenue= the unit price (p) multiplied by unit sales (-p/2+1900)
Revenue = -0.5 (1900)2 +1900 (1900)
Maximum Revenue (R) = 1805000
Therefore, revenue follows a downward sloping parabola. Mathematically, the maximum revenue will be occurring midway such points that give R as 0. After factoring p=0, p/2= 1900 and p=3800 are the points. The maximum revenue will therefore occur when p=1900.
At this point the maximum revenue obtained is,
R= - (19002)/2 + 1900 X 1900
= 1805000
The recommendations to give to John Deere would include;
The function being calculated follows a parabola that is downward sloping. Therefore, a price increase of two dollars will lead to a single less sale. As suc...