Based on a rigorous analysis of the data provided, this report provides details with respect to the profit-maximizing average daily production capacity for DermaPlusTM for each possible reference-based price of $50, $100, and $150 per unit identified by the consultant. The estimated expected daily profit at each price will also be provided. All unit and price values have been rounded to the nearest whole number or dollar.
Information in terms of the recommended average daily production capacity in units for the next 12 months will be provided in order to set the size of the plant’s unionized workforce. The assumption is the quantity of units identified used to set the size of the workforce will maximize daily profit.
A summary and recommendations to management will follow the analysis.
Profit-Maximizing Average Daily Production Capacity & Expected Profit
Biomed operates in a perfectly competitive market and has no degree of price setting power. In this case of DermaPlusTM, the government sets the price of the product. In order to determine the profit maximizing output in the short-run for this market, each price level provided by the consultant must be equal to the short-run marginal cost.
Total profit is calculated from subtracting the combined total fixed and variable costs from the total revenue generated. Total costs are derived from the fixed cost of $9,000 in addition to calculating the average variable cost formula provided by the regression analysis multiplied by the profit-maximizing average daily production capacity calculated at each price level.
The regression analysis provided by Selwyn based on the data collected is statistically significant greater than a 99% confidence level based on the p-value with a high correlation between the dependent and independent variables at 95%
Refer to Appendix I for the detailed calculations for profit-maximizing average daily production capacity and expected profit.
Price Level = $50 per unit
If the government sets the price of DermaPlusTM at this level, BioMed’s profit maximizing average daily production capacity is 342 units. At this level of output, total revenue generated is $17,100 per day. The total cost of producing this level of output based on total fixed and variable costs is $17,349. BioMed incurs a loss of $249 per day when the price is set at $50 per unit.
If the price is set at $50 per unit by the government, BioMed should still continue to produce this product if production is set at 342 units. Based on the shutdown rule, BioMed can sell at a loss for the next twelve months as the selling price at $50 per unit is greater than the minimum average variable cost of $22.47.
Price Level = $100 per unit
The profit-maximizing average daily production capacity at $100 per unit is 407 units. At this level of production, total revenue generated per day is equal to $40,700 with a total cost of $22,125. This level of daily production will yield a profit of $18,575.
Price Level = $150 per unit
At $150 per unit, the profit-maximizing average daily production capacity is 456 units. Total revenue generated at this level is equal to $68,400 at a total cost of $28,210. A profit of $40,190 per day is achieved when pricing is set at this level.
Recommended Average Daily Production Capacity – 12 Months Based on Price Uncertainty
The recommended average daily production capacity will be calculated using the expected price based on the probability distribution calculated by the outcome of the weighted averages. According to the consultant, there is a 5% chance of price being set at $50, a 20% chance of the price being set at $100, and a 75% chance of the price being set at $150. As a result, the price expected (Pe) based on the information from the consultant is $135 per unit.
At this expected price, the average daily production capacity should be set at 442 units generating at total revenue of $59,670 at a total cost of $26,219. At this level of production, profit should be maximized yielding a total profit of $33,451.
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