Hoodie Order for the Senior Trip
A student club is selling hoodies to fund a senior trip. The printer charges a $180 setup fee plus $14.00 per hoodie for orders under 50, and $11.50 per hoodie for orders of 50 or more. The club plans to sell each hoodie for $30. The club treasury holds $600, and the adviser has told the club they must show a profit of at least $750 before the trip deposit is due. A member proposes: "Let's order 50 so we get the cheaper price, pay with the treasury, and we'll be fine." Hoodies cannot be returned, and unsold stock is the club's loss.
1. Using only the $600 treasury, what is the largest order the club can actually pay for? Does the 50-hoodie plan work?
Read the worked answer
Test the tier the quantity falls in - do not assume the volume price applies.
Under 50: 180 + 14.00n ≤ 600 → 14n ≤ 420 → n ≤ 30. So 30 hoodies cost 180 + 420 = $600 exactly.
50 or more: the cheapest qualifying order is 50 hoodies: 180 + 11.50(50) = 180 + 575 = $755.
Conclusion: $755 > $600, so the club cannot buy into the volume tier with treasury money alone. The maximum affordable order is 30 hoodies. The member's plan fails by $155 and would break the cash constraint even though the unit price is lower - a lower unit price does not help if the total bill cannot be paid.
2. At a $30 selling price, how many hoodies must be sold to break even, and how many must be ordered and sold to reach the $750 profit target? Use the correct price tier for each answer.
Read the worked answer
Break-even (n < 50): revenue = cost → 30n = 180 + 14n → 16n = 180 → n = 11.25 → 12 hoodies (must round up; 11 gives 330 vs. 334, a loss of $4).
Profit target: profit = 30n − (180 + 14n) = 16n − 180. Set 16n − 180 = 750 → n = 58.125, which is ≥ 50, so the tier price applies and the equation must be redone.
Redo with the 50+ price: profit = 30n − (180 + 11.50n) = 18.5n − 180. Set 18.5n − 180 = 750 → 18.5n = 930 → n = 50.27 → 51 hoodies.
Check: 51 × $30 = $1,530 revenue; cost = 180 + 11.50(51) = 180 + 586.50 = $766.50; profit = $763.50, which clears $750. Note that 50 hoodies yields only 1,500 − 745 = $745, just missing the target - the answer is 51, not 50.
3. The club orders 51 hoodies by collecting pre-order money. If only 78% of the hoodies sell at the $30 price and the rest are unsellable, what price per hoodie is needed on the ones that do sell to still clear $750?
Read the worked answer
Units sold: 0.78 × 51 = 39.78, so at most 39 whole hoodies sell (40 would exceed 78%; use 39 to be conservative).
Cost is fixed at the full order: 180 + 11.50(51) = $766.50.
Revenue required: 766.50 + 750 = $1,516.50.
Required price: 1,516.50 ÷ 39 = $38.88 → about $38.90 per hoodie.
Check: 39 × $38.90 = $1,517.10; profit = 1,517.10 − 766.50 = $750.60 ✓.
Judgment: a jump from $30 to $38.90 (about a 30% increase) is unlikely to sell, so the safer plan is to take firm pre-orders first and order only what is committed, rather than ordering 51 and absorbing unsold stock.