1. 2. Suppose that thousand a commodity commodity are sold each month when the p

Question

1.

2.

Suppose that thousand a commodity commodity are sold each month when the price is p dollars per particular x). The total monthly consumer unit, expenditure E is the total amount of money consumers spend each month. Determine the market price that generates the greatest total monthly consumer expenditure and the number of units sold during each month at the optimal price using the following information: The total monthly expenditure E as a function of p is given as E (p) -200p 36,000 p and represented on the graph below. 1600000 14000000 12000000 10000000 50 500 150 200 The optimal price is s The number of units sold monthly at the optimal price is

Explanation / Answer

E = -200p^2 + 36000p

E'(p) = -400p + 36000

Now, equate derivative to 0 :
-400p + 36000 = 0

400p = 36000

p = 36000/400

p = 90

So, the optimal price is : 90 dollars ----> ANSWER

Number of units sold :
90 = 5(36 - x)
18 = 36 - x
x = 18

So, the number of units : 18000 ----> ANSWER

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2)

Draw a vertical starting from x = 4 on the x-axis
as in, draw the line x = 4

Does the line hit the graph at more than one point?

Yes it does

So, bvertical line test fails

Not a function

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