Profit Optimization Through Product Mix Analysis

Analysis of Product Mix for Optimum Operating Income

Optimizing operating income through product mix analysis requires a strategic approach to balancing sales prices, variable costs, and machine hour constraints. In this scenario, we are presented with data on two types of lamps: Bedford Lamp and Lowell Lamp.

The sales price for Bedford Lamp is $25 per unit, while Lowell Lamp is priced at $35 per unit. On the other hand, the variable costs for Bedford Lamp amount to $17 per unit, and for Lowell Lamp, the variable costs are $23 per unit. Additionally, the machine hour requirements are 2 hours for Bedford Lamp and 4 hours for Lowell Lamp.

By calculating the contribution margin per unit for each type of lamp, we find that Bedford Lamp yields a higher contribution margin of $8 per unit compared to Lowell Lamp's $12 per unit. However, considering the machine hour constraints, Bedford Lamp utilizes 2 hours per unit whereas Lowell Lamp requires 4 hours per unit.

Given the total machine hour capacity of 25,000 hours per year, we must allocate these hours efficiently based on the product mix to maximize operating income. The analysis shows that producing 8,000 units of Bedford Lamps (16,000 machine hours) and 2,250 units of Lowell Lamps (9,000 machine hours) will result in the optimum operating income.

Therefore, the recommended product mix for achieving the highest operating income is 8000 units of Bedford Lamps and 2250 units of Lowell Lamps, as it utilizes the available machine hours effectively and considers the contribution margin per constraint.