Flour constraint, a special order and labour variances in a bakery
Angkor Bakery produces two products from a single flour supply limited to 20,000 kg per month. Product A uses 2 kg and earns contribution of $6 per unit; Product B uses 5 kg and earns contribution of $11 per unit. Monthly demand is 6,000 units of A and 3,000 units of B. A foreign retailer has offered to buy 500 units of B at $22 each; the normal selling price is $30 and variable cost is $19. The offer would require 2,500 kg of flour and would not affect normal demand if capacity were available, but flour supply cannot be increased before next year. Actual labour for 6,500 units was 1,800 hours at $4.20; standard is 0.25 hours per unit at $4.00.
1. Determine the optimal monthly production plan and total contribution under the flour constraint.
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Rank the products by contribution per kg of the scarce resource. Product A: $6 ÷ 2 kg = $3.00 per kg. Product B: $11 ÷ 5 kg = $2.20 per kg. Product A therefore ranks first. Produce all 6,000 units of A, using 12,000 kg and earning $36,000. The remaining 8,000 kg is used for B: 8,000 ÷ 5 = 1,600 units, earning 1,600 × $11 = $17,600. Total contribution = $36,000 + $17,600 = $53,600. Demand for B of 3,000 units is not fully met, but that is optimal given the constraint because A earns more per kg. The plan should be reconsidered if flour prices, selling prices or the product mix change; qualitative factors such as customer relationships and contractual minimum supplies to B customers also matter.
2. Evaluate the special order using relevant costing and opportunity cost.
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The special order contribution is $22 − $19 = $3 per unit, or $1,500 for 500 units. Flour is the binding constraint, so the relevant cost is the contribution forgone from the best alternative use of 2,500 kg. The optimal plan already leaves normal B demand unsatisfied; the marginal use of flour is normal B, earning $11 per 5 kg, or $2.20 per kg. Opportunity cost of 2,500 kg = 2,500 × $2.20 = $5,500. Net effect = $1,500 − $5,500 = −$4,000. Re-optimising confirms this: A remains at 6,000 units; the 8,000 kg available for B must now cover 500 special units plus normal B, leaving 5,500 kg for 1,100 normal B units. Contribution becomes $36,000 + $12,100 + $1,500 = $49,600, which is $4,000 lower than $53,600. Reject the order unless non-financial benefits, such as market entry or a future price premium, justify the loss.
3. Calculate the labour rate and efficiency variances and suggest likely causes.
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Actual labour cost = 1,800 hours × $4.20 = $7,560. Standard hours for 6,500 units = 6,500 × 0.25 = 1,625 hours; standard cost = 1,625 × $4.00 = $6,500. Total variance = $7,560 − $6,500 = $1,060 unfavourable. Rate variance = (actual rate − standard rate) × actual hours = ($4.20 − $4.00) × 1,800 = $360 unfavourable. Efficiency variance = (actual hours − standard hours) × standard rate = (1,800 − 1,625) × $4.00 = $700 unfavourable. Possible causes of the rate variance include a wage increase, overtime premium, or use of higher-grade staff. The efficiency variance may reflect untrained workers, machine breakdowns, poor scheduling, or lower-quality flour requiring more handling. The variances should be investigated together because paying a higher rate for more skilled staff could reduce wasted hours; the net effect, not each variance in isolation, should drive action.