Questions: Contain - It produces plastic storage bins for household storage needs. The company makes two sizes of bins: Large (50 gallon) and Regular (35 gallon). Demand for the product is so high that the company can sell as many of each size as it can produce. The same machinery is used to produce both sizes. The machinery is available for only 3,400 hours per period. The company can produce 12 Large bins every hour compared to 15 Regular bins in the same time. Fixed expenses amount to 120,000 per period. Sales prices and variable costs are as follows: 1. Which product should Contain - It emphasize? Why? 2. To maximize profits, how many of each size bin should the company produce? 3. Given this product mix, what will the company's operating income be? Costs - Regular Large Sales price per unit. 8.70 10.90 Variable cost per unit 3.20 4.10

Solution Steps

To determine which product Contain-It should emphasize, we need to calculate the contribution margin per machine hour for both Regular and Large bins. The contribution margin per unit is the sales price per unit minus the variable cost per unit. Then, we multiply the contribution margin per unit by the number of units produced per machine hour to get the contribution margin per machine hour. The product with the higher contribution margin per machine hour should be emphasized.

To maximize profits, we need to allocate the available machine hours to produce the bins in a way that maximizes the total contribution margin. Given the constraints, we can use linear programming to determine the optimal number of each size bin to produce.

Finally, we can calculate the company's operating income by subtracting the fixed expenses from the total contribution margin.

The contribution margin per unit for each bin type is calculated as follows:

For Regular bins: \[ CM_{\text{Regular}} = SP_{\text{Regular}} - VC_{\text{Regular}} = 8.70 - 3.20 = 5.50 \]

For Large bins: \[ CM_{\text{Large}} = SP_{\text{Large}} - VC_{\text{Large}} = 10.90 - 4.10 = 6.80 \]

Next, we calculate the contribution margin per machine hour:

For Regular bins: \[ CMH_{\text{Regular}} = CM_{\text{Regular}} \times \text{Units per hour}_{\text{Regular}} = 5.50 \times 15 = 82.50 \]

For Large bins: \[ CMH_{\text{Large}} = CM_{\text{Large}} \times \text{Units per hour}_{\text{Large}} = 6.80 \times 12 = 81.60 \]

To maximize profits, we allocate the available machine hours (3,400 hours) to produce Regular bins exclusively, as it has the higher contribution margin per machine hour. The optimal number of Regular bins produced is: \[ \text{Optimal Regular bins} = \text{Machine hours available} \times \text{Units per hour}_{\text{Regular}} = 3400 \times 15 = 51000 \]

The optimal number of Large bins produced is: \[ \text{Optimal Large bins} = 0 \]

The total contribution margin is calculated as follows: \[ \text{Total CM} = (\text{Optimal Regular bins} \times CM_{\text{Regular}}) + (\text{Optimal Large bins} \times CM_{\text{Large}}) = (51000 \times 5.50) + (0 \times 6.80) = 280500 \]

The operating income is then calculated by subtracting fixed expenses: \[ \text{Operating Income} = \text{Total CM} - \text{Fixed Expenses} = 280500 - 120000 = 160500 \]

Final Answer