3. Bulk Order Discounts (4 points)

Clubs often do some buying and selling during fundraisers, working with a vendor to make mugs, T-shirts, hoodies etc. that display the club's logo. There can be big savings for bulk orders. DiscountMug$

(http://www.discountmugs.com) is an on-line company with this kind of service. Suppose a high school group orders T-shirts for a fundraiser. The table below shows the pricing shown on the website. Note that the fixed cost involved in setting up the printing with the logo is absorbed into the pricing schedule.

Quantity 12+ 24+ 36+ 72+ 144+ 288+ 576+ 1008+ 2016+

Cost per T $5.55 $4.90 $4.86 $4.73 $4.62 $4.58 $4.42 $4.01 $3.59

a) We have seen problems for which breaking even was the goal, but in the context of fundraising the idea of break-even is not really the point! The goal may be to raise enough funds for, say, the choir to take part in an out of state competition, or for the Odyssey of the Mind team to go to World's.

i) If the club is comfortable charging $8 per T-shirt how many must be sold to raise $1000?

ii) If the club is comfortable charging $10 per T-shirt how many must be sold to raise $1000?

b) If the club can only sell 50 T-shirts what price must be charged in order to get the $1000?

c) Are problems involving bulk order discounts linear models? Or are they nonlinear? Explain you reasoning.