Moon Ltd. produces products 'X', 'Y', and 'Z' and has decided to analyze its production mix for these products. Direct Materials Rs. (per unit): X: 160, Y: 120, Z: 80 Variable Overheads Rs. (per unit): X: 8, Y: 20, Z: 12 Direct Labour: Departments: Rate per Hour (Rs.), Hours per unit for X, Y, Z Department-A: 4 Rs/hr, 6 hrs (X), 10 hrs (Y), 5 hrs (Z) Department-B: 8 Rs/hr, 15 hrs (X), 11 hrs (Y), no data for Z Current Budget Details: Annual Production (units): X: 10,000, Y: 12,000, Z: 20,000 Estimated Selling Price per unit (Rs.): X: 312, Y: 400, Z: 240 Sales department estimate of possible sales in the coming year (units): X: 12,000, Y: 16,000, Z: 24,000 There is a constraint on labor supply in Department-A; manpower cannot be increased beyond the present level. Required: (i) Identify the best possible product mix of Moon Ltd.
Answer (1)
To determine the best product mix for Moon Ltd., we need to analyze the contribution margin for each product and the constraint on labor supply in Department-A.
Step 1: Calculate the Contribution Margin
The contribution margin per unit for each product is calculated as follows:
Product X
Selling Price per unit: Rs. 312
Direct Materials: Rs. 160
Variable Overheads: Rs. 8
Direct Labour (Dept-A): 6 hrs × Rs. 4/hr = Rs. 24
Direct Labour (Dept-B): 15 hrs × Rs. 8/hr = Rs. 120
Total Variable Cost = Rs. 160 + Rs. 8 + Rs. 24 + Rs. 120 = Rs. 312
Contribution Margin per unit = Selling Price - Total Variable Cost = Rs. 312 - Rs. 312 = Rs. 0
Product Y
Selling Price per unit: Rs. 400
Direct Materials: Rs. 120
Variable Overheads: Rs. 20
Direct Labour (Dept-A): 10 hrs × Rs. 4/hr = Rs. 40
Direct Labour (Dept-B): 11 hrs × Rs. 8/hr = Rs. 88
Total Variable Cost = Rs. 120 + Rs. 20 + Rs. 40 + Rs. 88 = Rs. 268
Contribution Margin per unit = Selling Price - Total Variable Cost = Rs. 400 - Rs. 268 = Rs. 132
Product Z
Selling Price per unit: Rs. 240
Direct Materials: Rs. 80
Variable Overheads: Rs. 12
Direct Labour (Dept-A): 5 hrs × Rs. 4/hr = Rs. 20
Total Variable Cost = Rs. 80 + Rs. 12 + Rs. 20 = Rs. 112
Contribution Margin per unit = Selling Price - Total Variable Cost = Rs. 240 - Rs. 112 = Rs. 128
Step 2: Assessing the Labour Constraint in Department-A
Since manpower cannot be increased, the available labor hours are a constraint. We should produce products that provide the highest contribution margin per labor hour in Department-A.
Contribution Margin per labor hour in Dept-A
Product X: Rs. 0 / 6 hrs = Rs. 0
Product Y: Rs. 132 / 10 hrs = Rs. 13.2
Product Z: Rs. 128 / 5 hrs = Rs. 25.6
Step 3: Determine Optimal Product Mix
With a constraint in Department-A and aiming to maximize the contribution margin per labor hour, the best approach is:
Prioritize production of Product Z (highest contribution margin per labor hour: Rs. 25.6).
If there are remaining labor hours after fulfilling potential sales for Z, produce Product Y (next best option with Rs. 13.2 per hour).
No units of Product X should be produced as it provides no contribution margin.
Conclusion
Given the constraint in Department-A, Moon Ltd. should focus on maximizing the production of Product Z first due to its highest efficiency in labor utilization, followed by Product Y, and avoid Product X as it doesn’t contribute positively to the profit per labor hour available.
