T-shirt printing: is a P36 order worth taking?
Tlotlo prints T-shirts to pay for school fees. The screen-printing kit cost P450 once, and each shirt uses P28 of blank shirt and ink. He sells shirts at P45 and reliably sells 40 shirts a month. Because of school and homework he can print no more than 60 shirts in a month. A football club has offered to buy 25 shirts at P36 each, but they want them this month, so any shirts he prints for the club reduce the number he can print for his regular customers. Tlotlo's friend says, 'P36 is more than P28, so take it - you make P8 on every shirt.' Tlotlo is not sure, because he would have to give up some full-price sales.
1. Calculate Tlotlo's break-even number of shirts at P45 and his current monthly profit.
Read the worked answer
Profit = (price − cost per shirt) × number sold − fixed cost.
Contribution per shirt = 45 − 28 = P17. This is what each shirt contributes towards the P450 kit.
- Break-even: 450 ÷ 17 = 26.47, so he needs 27 shirts. At 26 shirts he recovers 26 × 17 = P442 and is P8 short; the 27th shirt takes him past the fixed cost.
- Current sales: 40 × 17 = P680 contribution, so profit = 680 − 450 = P230 per month.
Note that the P450 is a one-off: it is only a barrier until it is recovered. After 27 shirts, every extra shirt adds the full P17.
2. Should Tlotlo accept the 25 shirts at P36? Answer with a capacity and contribution argument, not just a margin.
Read the worked answer
The P8 margin is real but incomplete, because the resource that is short is not money - it is printing time. Capacity is 60 shirts, and regular demand is already 40, so only 20 shirts of spare capacity exist.
- Regular contribution: 40 × 17 = P680.
- With the order he prints 60 in total, so he can supply only 60 − 25 = 35 regular shirts. Contribution = 35 × 17 + 25 × (36 − 28) = 595 + 200 = P795.
- Change = 795 − 680 = +P115. Profit rises from P230 to P345.
Accept the order - but for the right reason: the club shirts earn P8 each on capacity that would otherwise be idle, and displacing 5 full-price shirts costs only 5 × 17 = P85, which is less than the P200 gained. The friend's reasoning would also 'justify' accepting P29 shirts, which would be wrong. If regular demand were already 60, the order would cost 25 × 17 = P425 and gain P200, a loss of P225 - he should then refuse.
3. Find the lowest price per shirt at which the club order still leaves Tlotlo better off than refusing it, and comment on the result.
Read the worked answer
Let the club price be p. The order gains 25(p − 28) and loses 5 regular sales worth 5 × 17 = 85.
25(p − 28) = 85 p − 28 = 3.40 p = P31.40
At P31.40 the two options are exactly equal (profit P230 either way); above P31.40 the order is better; below it he should refuse. Check: 25 × (31.40 − 28) = 25 × 3.40 = P85, exactly the lost regular contribution.
Comment: the floor price is P31.40, not P28. 'Any price above cost' is wrong whenever capacity is limited - the true cost of a club shirt includes the full-price shirt it pushes out. P31.40 is also well below his normal P45, so a big discount is affordable only because 20 shirts of capacity are idle. If the club became a regular customer, he would need to raise the price towards P45. Non-financial points worth weighing: prompt payment risk, whether the club advertises his work, and wear on the equipment.