The following data relates to three products manufactured by BJS Ltd:PRODUCT X Y ZSelling price per unit ($) 12 16 14Direct Material cost per unit 3 10 7Maximum demand (units) 15,000 40,000 20,000Time required on the bottleneck(hours per unit) 3 1.5 7The firm has 80,000 bottleneck hours available each period.Total factory costs amount to $100,000 in the period.REQUIRED:a. Calculate the optimum product mix and the maximum profit.b. Calculate the throughput accounting ratio for each product
Question
The following data relates to three products manufactured by BJS Ltd:PRODUCT X Y ZSelling price per unit (100,000 in the period.REQUIRED:a. Calculate the optimum product mix and the maximum profit.b. Calculate the throughput accounting ratio for each product
Solution
a. To calculate the optimum product mix and the maximum profit, we first need to calculate the contribution per bottleneck hour for each product. This is done by subtracting the direct material cost per unit from the selling price per unit, and then dividing by the time required on the bottleneck.
For product X: Contribution per bottleneck hour = (12 - 3) / 3 = $3 per hour
For product Y: Contribution per bottleneck hour = (16 - 10) / 1.5 = $4 per hour
For product Z: Contribution per bottleneck hour = (14 - 7) / 7 = $1 per hour
The product with the highest contribution per bottleneck hour should be produced first, until its maximum demand is met. Then, the product with the next highest contribution should be produced, and so on. Therefore, the optimum product mix is Y, X, Z.
To calculate the maximum profit, we multiply the contribution per bottleneck hour by the maximum demand for each product, and then subtract the total factory costs.
Maximum profit = (4 * 40,000) + (3 * 15,000) + (1 * 20,000) - 100,000 = 45,000 + 100,000 = $125,000
b. The throughput accounting ratio for each product is calculated by dividing the contribution per bottleneck hour by the selling price per unit.
For product X: Throughput accounting ratio = 3 / 12 = 0.25
For product Y: Throughput accounting ratio = 4 / 16 = 0.25
For product Z: Throughput accounting ratio = 1 / 14 = 0.071
Therefore, the throughput accounting ratios for products X, Y, and Z are 0.25, 0.25, and 0.071 respectively.
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