Feed Money That Will Not Stretch to the End of the Month
Mr Kativa is preparing for the NUST entrance tests and also runs a small flock of 400 laying hens that must be fed every day. Each bird eats 120 g of feed per day. Feed is sold only in 25 kg bags at N$ 385 per bag, and the supplier gives a 5% discount on any single order of 20 bags or more. His working month has 30 days. He has N$ 12 000 in cash, but before he may spend anything on feed he must pay N$ 2 300 for transport and N$ 1 400 for a vaccination that is already booked. He holds no feed stock, has no credit account, and cannot borrow. Whatever he does not buy today he must buy later at the same price. Eggs are collected daily but paid for weekly, so some money will come in, though not before the end of the week. He asks you to check his figures before he places the order.
1. Calculate the flock's feed requirement for the full 30 days in kilograms and in bags, the full cost of that feed, and the number of days of feed Mr Kativa can actually pay for today.
Read the worked answer
Step 1 - daily demand. 400 birds × 0.120 kg = 48 kg per day.
Step 2 - monthly demand. 48 kg × 30 days = 1 440 kg.
Step 3 - bags. 1 440 ÷ 25 = 57.6. Feed is not sold loose, so 58 bags are needed for the month.
Step 4 - full cost. 58 bags qualify for the 5% discount (58 ≥ 20): 58 × N$ 385 = N$ 22 330; × 0.95 = N$ 21 213.50.
Step 5 - cash genuinely free for feed. N$ 12 000 − (N$ 2 300 + N$ 1 400) = N$ 8 300. The vaccination and transport are committed costs, so they cannot be counted as feed money.
Step 6 - bags affordable. One discounted bag costs N$ 385 × 0.95 = N$ 365.75. N$ 8 300 ÷ N$ 365.75 = 22.69, so 22 bags (23 bags would cost N$ 8 412.25, which he does not have). The discount still applies because 22 ≥ 20.
Conclusion. 22 bags = 550 kg = 550 ÷ 48 = 11.45, so about 11 full days of feed. He is short N$ 12 913.50 for the month. The honest answer to his question is no: cash on hand covers roughly a third of the month, so a second purchase must be planned before day 11.
2. Mr Kativa intends to order exactly 20 bags because 'round numbers are safer'. Compare 20 bags with 22 bags and advise him which to order, given that the egg money arrives at the end of the week.
Read the worked answer
20 bags: 20 × 25 = 500 kg → 500 ÷ 48 = 10.4 days. Cost 20 × N$ 365.75 = N$ 7 315, leaving N$ 985 in hand.
22 bags: 550 kg → 11.46 days. Cost N$ 8 046.50, leaving N$ 253.50.
The trade-off in one line: N$ 731.50 buys 50 kg, which is 1.04 days of feed, so the extra two bags are not wasteful - 50 kg at the discounted rate is N$ 14.63/kg, against N$ 15.40/kg at list price (a full day at list costs 48 × 15.40 = N$ 739.20).
But the buffer matters. The 20-bag order leaves N$ 985 for anything unplanned: a transport breakdown, a bag damaged in storage, a price change before the next purchase. The 22-bag order leaves N$ 253.50, which is less than one discounted bag.
Recommendation. The 'round number' argument is not a reason; 20 bags is chosen for the cushion, not the roundness. If the egg payment is reliable and arrives within seven days, order 22 bags and accept the thin buffer, because every extra day of cover reduces the risk that the birds go unfed before the next order. If the egg payment has ever been late, order 20 bags and keep N$ 985. Either way, he should never order 19 bags: dropping below the threshold costs him N$ 19.25 per bag, about N$ 385 across a 20-bag order, for nothing.
3. Mr Kativa cannot raise more cash this week. Recommend a plan for the next 11 days, supporting each element with a calculation, and identify the risk that would make you change the plan.
Read the worked answer
Option A - buy 22 bags now, order again before day 11. This is the baseline. It needs a second order of at least 20 bags to keep the 5% discount, which means finding N$ 7 315 from egg sales within about 10 days. Feasible only if the weekly egg payment is at least that size.
Option B - cut the flock. Selling 60 hens leaves 340 birds: 340 × 0.12 = 40.8 kg/day, so 550 ÷ 40.8 = 13.5 days from the same 550 kg - about two extra days - plus cash from the sale of the birds.
Option C - cut waste. If spillage and scatter are reduced so intake falls from 120 g to 110 g per bird, demand drops to 44 kg/day and 550 ÷ 44 = 12.5 days. This is the cheapest gain because it costs nothing.
Option D - ask the supplier for seven days' credit on a 20-bag order, in writing, so the discount survives.
Recommended combination, in order: buy 22 bags today (it is the most feed the cash allows and keeps the discount), cut waste immediately (Option C), and approach the supplier for credit this week rather than waiting until the feed runs out. Underfeeding layers is the one error that cannot be recovered quickly - a shortfall cuts egg production for weeks, which damages the very income meant to fund the next order.
What would change the plan: if the egg buyer confirms in writing that payment will be late, sell the 60 surplus hens first and buy 20 bags, keeping the N$ 985 cushion. Speed of cash, not the price of feed, is the binding constraint.