Choosing a Maize Plot within Budget
A family in Bafoussam has a budget of 3,000,000 XAF to buy a small maize plot and pay for the first season. Plot A is rectangular, 45 m by 28 m, and costs 2,400,000 XAF. Plot B is a trapezium with parallel sides 38 m and 52 m, perpendicular height 30 m, and the two other sides measure 32 m and 34 m; it costs 2,700,000 XAF. Fencing costs 2,500 XAF per metre. Ploughing, seed and fertilizer cost 100 XAF per square metre on either plot. Local trials give expected yields of 2.5 kg per square metre on Plot A and 2.8 kg per square metre on Plot B. Maize sells at 350 XAF per kg. The family must fence the chosen plot and meet all first-season costs from the same budget. They want to know which plot gives better value per square metre, which gives the higher net income after season costs, and which they can actually afford.
1. Calculate the area of each plot and the price per square metre. Which plot is better value per square metre?
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Plot A area = 45 × 28 = 1,260 m². Price per m² = 2,400,000 ÷ 1,260 ≈ 1,904.76 XAF. Plot B area = ((38 + 52) ÷ 2) × 30 = 45 × 30 = 1,350 m². Price per m² = 2,700,000 ÷ 1,350 = 2,000 XAF. Plot A is cheaper per square metre by about 95.24 XAF, or about 4.8% (95.24 ÷ 2,000 × 100). So Plot A is better value on land price alone.
2. Calculate fencing cost, other season costs, expected revenue and net income after season costs for each plot. Ignore the purchase price in this part.
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Plot A perimeter = 2(45 + 28) = 146 m. Fencing = 146 × 2,500 = 365,000 XAF. Other costs = 1,260 × 100 = 126,000 XAF. Season costs = 491,000 XAF. Yield A = 1,260 × 2.5 = 3,150 kg. Revenue = 3,150 × 350 = 1,102,500 XAF. Net after season costs = 1,102,500 − 491,000 = 611,500 XAF. Plot B perimeter = 38 + 52 + 32 + 34 = 156 m. Fencing = 156 × 2,500 = 390,000 XAF. Other costs = 1,350 × 100 = 135,000 XAF. Season costs = 525,000 XAF. Yield B = 1,350 × 2.8 = 3,780 kg. Revenue = 3,780 × 350 = 1,323,000 XAF. Net after season costs = 1,323,000 − 525,000 = 798,000 XAF. Plot B gives 186,500 XAF more net income after season costs.
3. Using the 3,000,000 XAF budget, decide which plot the family can buy and pay for. Advise them, taking both affordability and net income into account.
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Total cash needed for A = 2,400,000 + 491,000 = 2,891,000 XAF. This is within 3,000,000 XAF, leaving 109,000 XAF. Total cash needed for B = 2,700,000 + 525,000 = 3,225,000 XAF. This exceeds the budget by 225,000 XAF, so B cannot be bought without extra finance. If the family cannot borrow, they must choose A even though B has the higher season net income. If they can raise 225,000 XAF, B returns 186,500 XAF more after season costs, but the extra outlay is 334,000 XAF (3,225,000 − 2,891,000), so B does not fully repay the extra cash from the first season alone. B also provides 90 m² more land (1,350 − 1,260), which has lasting value. A is the safer budget choice; B is attractive only if the extra money is available on affordable terms.