Maximizing Profit for National Business Machines
What is the optimal number of units for National Business Machines to manufacture each month to maximize profit?
Given that each model a costs $100 to make, each model b costs $150, with profits of $25 for each model a and $40 for each model b portable printer. With a manufacturing cost limit of $600,000/month and a demand limit of 2500 portable printers per month, how many units of each model should National make each month to maximize profit?
Optimal Number of Units to Maximize Profit
The optimal number of units for National Business Machines to manufacture each month in order to maximize profit can be calculated by considering the manufacturing cost constraint, demand constraint, and profit function.
In order to maximize monthly profit, National Business Machines should determine the number of units of each model that will generate the highest profit. Let's assume the number of model a portable printers produced is x and the number of model b portable printers produced is y.
The manufacturing cost constraint can be expressed as 100x + 150y <= 600,000 and the demand constraint can be expressed as x + y <= 2500. The profit function can be expressed as P = 25x + 40y.
To find the optimal number of units of each model to manufacture, we need to plot the feasible region and identify the values of x and y that will maximize the profit. By solving these constraints and maximizing the profit function, National Business Machines can determine the optimal number of units of each model to produce per month.
By calculating the maximum profit, National Business Machines can ensure they are operating at peak efficiency and profitability while meeting both manufacturing cost and demand constraints.