Rice Trader's Packet Pricing
A market trader in Douala buys 8 bags of rice. Each bag contains 50 kg and costs 22,000 XAF. She pays 6,000 XAF in total for transport to her stall. While repacking the rice into 2 kg packets, 10 kg is spilled and cannot be sold. She plans to sell each 2 kg packet at 1,200 XAF. A hotel manager offers to buy every packet she can produce at 1,050 XAF per packet, provided she delivers them to the hotel; delivery would cost her 4,500 XAF in total. The trader expects that, if she sells at the stall, she will sell 80% of the packets at 1,200 XAF and the rest at a reduced price of 900 XAF near the end of the week. She wants to compare the hotel offer with her own retail plan and to know the lowest packet price that avoids a loss.
1. Find the number of 2 kg packets that can be sold, the trader's total cost, and the break-even price per packet to the nearest franc.
Read the worked answer
Mass bought = 8 × 50 = 400 kg. After the 10 kg spill, sellable mass = 390 kg. Packets = 390 ÷ 2 = 195. Total cost = (8 × 22,000) + 6,000 = 176,000 + 6,000 = 182,000 XAF. Break-even price = 182,000 ÷ 195 = 933.33 XAF per packet. To the nearest franc, she needs at least 934 XAF per packet to avoid a loss; 933.33 XAF is the exact break-even.
2. Calculate the expected profit under the stall plan. Use 80% of packets at 1,200 XAF and the rest at 900 XAF.
Read the worked answer
80% of 195 = 0.8 × 195 = 156 packets at 1,200 XAF. Revenue = 156 × 1,200 = 187,200 XAF. Remaining = 195 − 156 = 39 packets at 900 XAF. Revenue = 39 × 900 = 35,100 XAF. Total revenue = 187,200 + 35,100 = 222,300 XAF. Profit = 222,300 − 182,000 = 40,300 XAF. Profit percentage on cost = 40,300 ÷ 182,000 × 100 ≈ 22.1%.
3. Calculate the profit from the hotel offer and recommend which plan the trader should choose. Mention one risk the trader should consider.
Read the worked answer
Hotel revenue = 195 × 1,050 = 204,750 XAF. Extra delivery cost = 4,500 XAF. Total cost = 182,000 + 4,500 = 186,500 XAF. Profit = 204,750 − 186,500 = 18,250 XAF. Profit percentage = 18,250 ÷ 186,500 × 100 ≈ 9.8%. The stall plan gives a higher expected profit (40,300 XAF versus 18,250 XAF), so on these figures she should prefer the stall plan. The hotel offer is safer because it sells all 195 packets at once and avoids the risk of unsold stock or price cuts. The trader should choose the hotel only if she believes the 80% full-price sales are unlikely, or if she needs cash quickly. She should also check whether the hotel will pay promptly and whether the 4,500 XAF delivery cost is guaranteed.