Every Halloween, Peterson$$s Ice Cream Shop offers a trick$-$or$-$treat package of $25$ coupons for $$20.$ The coupons are redeemable by children $12$ years or under, for a single$-$scoop cone, with a limit of one coupon per child per visit. Coupon sales average $540$ books per year. The printing costs are $$67\mathrm{.}50.$ A single$-$scoop cone of Peterson$$s ice cream normally sells for $$2\mathrm{.}00.$ The variable costs of a single$-$scoop cone are $$1\mathrm{.}50.$

Required

a$.$ Determine the loss if all coupons are redeemed without any other effect on sales.

Note: Round your answer to the nearest whole dollar.

$Answer

b$.$ Assume all coupons will not be redeemed. With regular sales unaffected, determine the coupon redemption rate at which Peterson$$s will break even on the offer.

Note: Round your answer to the nearest full percentage point.

Answer

$\%$

c$.$ Assuming regular sales are not affected and one additional single$-$scoop cone is sold at the regular price each time a coupon is redeemed, determine the coupon redemption rate at which Peterson$$s will break even on the offer.

Note: Round your answer to the nearest full percentage point.

Answer

$\%$

d$.$ Determine the profit or loss incurred on the offer if the coupon redemption rate is $60\%$ and:

$1.$ One$-$fourth of the redeemed coupons have no effect on sales.

$2.$ One$-$fourth of the redeemed coupons result in additional sales of two single$-$scoop cones.

$3.$ One$-$fourth of the redeemed coupons result in additional sales of three single$-$scoop cones.

$4.$ One$-$fourth of the redeemed coupons come out of regular sales of single$-$scoop cones

Note: Round your answer to the nearest whole dollar.

$Answer