Final answer:
The maximum operating income the company can earn with the constraint of 3,000 machine-hours per month is $80,000, considering producing only pants due to their higher contribution margin per machine-hour.
Step-by-step explanation:
To calculate the maximum amount of operating income that the company can earn with only 3,000 machine-hours available per month, we need to determine the contribution margin per machine-hour for both products. For pants, the contribution margin per unit is $60 selling price minus $40 variable cost, which equals $20. Given that each pair of pants requires 0.20 machine-hours, the contribution margin per machine-hour for pants is $20 / 0.20 mh, or $100 per machine-hour. For shirts, the contribution margin per unit is $50 selling price minus $30 variable cost, which equals $20. With shirts requiring 0.25 machine-hours each, the contribution margin per machine-hour for shirts is $20 / 0.25 mh, or $80 per machine-hour. Since pants have a higher contribution margin per machine-hour, the company should produce pants to maximize profit until demand is satisfied or machine hours are exhausted. Therefore, the maximum operating income would be the contribution margin of pants multiplied by the number of units that can be produced with the available machine-hours, minus the fixed costs.
The demand for pants is 14,000 units, but with 3,000 mh available and each unit of pants requiring 0.20 mh, the maximum number of units of pants that can be produced is 3,000 mh / 0.20 mh/unit = 15,000 units. However, demand limits this to 14,000 units. So, the total contribution margin for pants would be 14,000 units * $20 = $280,000. Subtracting the fixed costs of $200,000 from this amount gives a maximum operating income of $80,000.