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P 194 Prob_22 Powerpoint Show

# P 194 Prob_22 Powerpoint Show - am company finds that at a...

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eam company finds that at a price of \$4.00, demand is 4000 units. For every \$0.25 d demand increases by 200 units. Find the price and quantity that maximize revenue. Answer must find a demand equation to determine the relationship between price and quant e our given information and make a chart. When q=4000, p=4.00. When the price g en quantity increases to q=4200. Let’s use “p” as the independent variable (normall as the dependent variable (normally “y”). 200 0.25 Let’s find the slope m = y x = 4000 - 4200 4.00 - 3.75 = - 200 0.25 = - 800 let’s find the y-intercept by plugging the “top” pair of coordinates into the equat ng into the general form of a linear equation (y=mx+b) gives us q=-800p+b q = - 800 p + b 4000 = - 800(4) + b 4000 = - 3200 + b 7200 = b p q 4.00 4000 3.75 4200 0 This gives us our demand function q = - 800 p + 7200 (Click mouse or hit any key to continue)

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t’s check this equation by plugging in our other set of coordinates 3.75 and 420 q = - 800 p + 7200 4200 = - 800(3.75) + 7200 4200 = - 3000 + 7200 4200 = 4200 Therefore our demand equation is correct! ow revenue is found by multiplying the \$/item (p) by the number of items (q). R = p q = p - 800 p + 7200 ( 29 = - 800 p 2 + 7200 p Next, take the derivative and set it equal to 0 to find the critical points.

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