6. Office Depot sells TI-84 Plus calculators for $200 each. In a typical August

Question

6. Office Depot sells TI-84 Plus calculators for $200 each. In a typical August (right before school starts) Office Depot sells 100,000 of these calculators. They are considering inereasing the price. For every $5 price increase, 1100 fewer calculators will be sold that month. a. (4 points) Define the function that models the total revenue to the company as a function of the number of $5 price increases. Answer Dind the sate prterthat way, ineraase by any dollaz anount, (not just by s's). find the sale price that will maximize the revenue. Round to the nearest cent Answer

Explanation / Answer

a)

6)

let the number of $5 increase in prices be x

price of calculator = 200 +5x

number of calculators sold = 100000 -1100x

revenue , R(x)=(200 +5x)(100000 -1100x)

(b)

R(x)=-5500x2 +280000x +20000000

R(x)=-5500(x2 -(560/11)x) +20000000

R(x)=-5500(x2 -(560/11)x +(280/11)2-(280/11)2) +20000000

R(x)=-5500(x2 -(560/11)x +(280/11)2)+5500(280/11)2 +20000000

R(x)=-5500(x -(280/11))2+(259200000/11)

revenue is maximised when x=280/11

sale price for maximum revenue =200 +5*(280/11)

sale price for maximum revenue =200 +127.27272727272727272727272727273

sale price for maximum revenue =327.27 dollars

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