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A music store sells regular CDs for $10.25. On average, the store sells 205 CDs every day. For each 80-cent increase in the price of regular CDs, the sales of CDs will go down by 8. What should the CD price be to get the most income from CD sales?

User BrentR
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1 Answer

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We have that the price of a regulat CD is $10.25

The store sells 205 CDs a day.

For each $0.8 increase in price, we have that the ammount of sold CDs decreasy by 8.

From this, we calculate the ammount of money they make each time they add $0.8 taking into account the disminution in buyers:

$10.25*205 = $2102.25

$11.05*197 = $2176.85

$11.85*189 = $2239.65

$12.65*181 = $2289.65

$13.45*173 = $2326.85

And we keep doing this until we get:

$15.05*157 = $2362.85

$15.85*149 = $2361.65

Now, from this we can see that the maximum value is between those prices, that since the total earning start to lower instead of increase. And since we also have that for each 0.8 increase in price we get 8 less buyers, we can deduce that for each 0.1 increase in price we get 1 less buyer. Therefore we proceed to determine in which price between $15.05 and $15.85 we get the maximum ammount of money:

$15.15*156 = $2363.4

$15.25*155 = $2363.75

$15.35*154 = $2363.9

$15.45*153 = $2363.85

From this, we have that the optimal price is $15.35 for ech CD. That, since it gives the maximum ammount of money before it starts to decrease.

User John Smithers
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