DellceCon is considering selling its delicious ice-cream cones using stands along Hot Beach, which is 5 miles long. According to its estimates, there are 1,000 sunbathers evenly spread along the beach and the each sunbather will buy one ice-cream cone per day pro - vided that the price plus any transportation (disutility) cost does not exceed $5. Each sunbather incurs a transportation (disutility) cost of leaving the comfort of their chair and umbrealla to get a cone and return to their spot of 25 cents per 0.25 mile. Each cone costs $0.50 to make and DeliceCon incurs a cost of $40 per day to run one of its stands. We would like to know how many stands DellceCon should operate and the price per cone that it should charge at each stand to maximize its profit.

The price per charged should be $2.5

Explanation:

Disutility cost per 0.25 mile is 25 cents. Therefore, the cost per mile is 4x25 cents = $1

The disutility for the entire 5 miles is $5. This implies that 1 stand can easily satisfy the

condition of the disutility not being more than $5.

Thus, the seller should operate 1 stand.

Now, the total transportation cost can be minimized if the stand is set up in the middle of

the beach. In that case, the sunbathers at the farthest two ends would face a cost of $2.5

(2.5 miles x $1)

This means that in order to satisfy the disutility condition, the total of the price charged,

and disutility incurred should be less than $5.

Therefore, $2.5 + Price < $5. This means that Price $2.5

In order to maximize the profits, he would charge the maximum possible price.

Thus, the price per charged should be $2.5