Question

A company manufactures two products, X and Y. Each unit of X requires 10 machine hours and each unit of Y requires 4 machine hours. The company's productive capacity is limited to 180,000 machine hours. Each unit of X sells for $15 and has variable costs of $7. Each unit of Y sells for $8 and has variable costs of $3. If the company can sell all that it produces of both products, what should the sales mix be? 50% X and 50% Y 60% X and 40% Y 75% X and 25% Y 90% X and 10% Y

Answer 1

To determine the sales mix, we need to calculate the contribution margin per product. For product X, the contribution margin is $8 and for product Y, the contribution margin is $5. The sales mix should be 60% X and 40% Y.

Step-by-step explanation:

To determine the sales mix, we need to calculate the contribution margin per product. The contribution margin is the difference between the selling price and the variable cost per unit. For product X, the contribution margin is $15 - $7 = $8. For product Y, the contribution margin is $8 - $3 = $5. Now, let's calculate the ratio of the contribution margin for each product:

Product X: $8 / ($8 + $5) = 0.6154 (rounded to four decimal places)

Product Y: $5 / ($8 + $5) = 0.3846 (rounded to four decimal places)

The sales mix should be 61.54% X and 38.46% Y. Therefore, the closest option to this ratio is 60% X and 40% Y.

Answer 2

The sales mix should be 75% X and 25% Y to maximize profitability.

Step-by-step explanation:

The company should use a sales mix of 75% X and 25% Y.

To determine the sales mix, we need to compare the contribution margin per machine hour for each product. The contribution margin for X is $8 ((15-7)/10) per machine hour, and the contribution margin for Y is $1.25 ((8-3)/4) per machine hour.

Since X has a higher contribution margin per machine hour, it is more profitable to allocate more machine hours to X. By allocating 75% of the machine hours to X and 25% to Y, the company can maximize its profitability.