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When operating at capacity, operating income is maximized by maximizing contribution margin per unit of the resource that is limiting either the production or the sale of products. The contribution margin per unit of Product X is $24. Product X requires 8 lbs. of raw materials per unit. Therefore, the contribution margin per unit of raw materials for Product X is $24 / 8, or $3. The contribution margin per unit of Product Y is $50. Product Y requires 10 lbs. of raw materials per unit. Therefore, the contribution margin per unit of raw materials for Product Y is $50 / 10, or $5. Since the contribution margin per unit of raw materials used is higher for Product Y than for Product X, the company should use all of its raw materials to produce Product Y, assuming demand is sufficient to enable the company to sell all of the Product Y it produces. Since 1,200 pounds of raw material are available and each unit of Product Y requires 10 pounds of material, Specialty Inc. will be able to produce 120 units of Product Y (1,200 ÷ 10).
This combination of production for Products X and Y is not possible given the amount of raw material that is available.
When operating at capacity, operating income is maximized by maximizing contribution margin per unit of the resource that is limiting either the production or the sale of products. While it is possible for the company to produce 150 units of X with 1,200 pounds of raw materials, this would not maximize contribution margin.
When operating at capacity, operating income is maximized by maximizing contribution margin per unit of the resource that is limiting either the production or the sale of products. While it is possible for the company to produce 100 units of Product X and 40 units of Product Y, this would not maximize contribution margin.