Chapter 23: Sales Mix When Resources Constrained

Determining Sales Mix with Constrained Resources When a company sells multiple products but faces limited production capacity, determining the optimal sales mix becomes crucial. The goal is to maximize the total contribution margin by prioritizing products that provide the highest contribution margin per unit of the constrained resource (e.g., machine hours, labor hours). Key Concepts: • • • Contribution Margin (CM) per Unit: The difference between the selling price and variable costs of a product. CM per Unit=Selling Price−Variable Costs Contribution Margin per Unit of Constrained Resource: This is calculated by dividing the contribution margin per unit by the number of constrained resource units (e.g., machine hours) required to produce one unit. CM per Unit of Constrained Resource=CM per UnitResource Units Require d per Unit Decision Rule: Produce the product with the highest contribution margin per unit of constrained resource until its demand is met. Use remaining capacity to produce the product with the next highest contribution margin per unit of the constrained resource. Example Scenario: Gamma and Omega A company produces two products, Gamma and Omega, with the following details: • • • • Gamma: o Selling Price: $10 per unit o Variable Costs: $7 per unit o Uses 1 machine hour per unit. Omega: o Selling Price: $12.50 per unit o Variable Costs: $8 per unit o Uses 3 machine hours per unit. Machine Hour Capacity: 5,000 machine hours per month. Demand: Gamma is limited to 3,800 units per month. Step 1: Compute the Contribution Margin per Unit for Each Product 1. Gamma: CM per Unit for Gamma=$10−$7=$3 2. Omega: CM per Unit for Omega=$12.50−$8=$4.50 Step 2: Compute Contribution Margin per Machine Hour 1. Gamma: o Machine Hours Required per Unit: 1 machine hour. o CM per Unit of Constrained Resource (Machine Hour): $31 MH=$3 per MH 2. Omega: o Machine Hours Required per Unit: 3 machine hours. o CM per Unit of Constrained Resource (Machine Hour): $4.503 MH=$1.50 per MH Step 3: Determine Optimal Production Mix • • • Gamma has a higher CM per machine hour ($3 per MH) compared to Omega ($1.50 per MH). Therefore, the company should produce Gamma first to meet its demand before switching to Omega. Production of Gamma: o Maximum Demand for Gamma: 3,800 units. o Machine Hours Required for Gamma: 3,800 units×1 MH per unit=3,800 MH3,800 o Producing 3,800 units of Gamma uses 3,800 machine hours, leaving: 5,000 MH Total−3,800 MH Used=1,200 MH Remaining Production of Omega with Remaining Capacity: o Machine Hours Available for Omega: 1,200 MH. o Machine Hours per Unit of Omega: 3 MH. o Units of Omega Produced: 1,200 MH3 MH per unit=400 units Step 4: Calculate the Total Contribution Margin from the Sales Mix 1. Contribution Margin from Gamma: o CM per Unit: $3. o Units Produced: 3,800. o Total CM from Gamma: 3,800 units×$3=$11,400 2. Contribution Margin from Omega: o CM per Unit: $4.50. o Units Produced: 400. o Total CM from Omega: 400 units×$4.50=$1,800 3. Total Contribution Margin: $11,400+$1,800=$13,200\$11,400 + \$1,800 = \$13,200$11,400+$1,800=$13,200 Solution Summary: • • The company should produce 3,800 units of Gamma and 400 units of Omega to maximize the contribution margin. Total Contribution Margin from the Optimal Sales Mix: $13,200. Decision Rule Recap: The company allocates its limited production capacity (machine hours) to produce Gamma first because it provides a higher contribution margin per machine hour. Once demand for Gamma is met, any remaining capacity is used to produce Omega. By using this approach, the company ensures that its resources are utilized in the most profitable way, maximizing overall profitability even when faced with production constraints.