Maximizing Profit for a Sporting Goods Manufacturer

How can a sporting goods manufacturer maximize profit?

To maximize profit, the company should manufacture 60 skateboards and 30 pairs of in-line skates.

A sporting goods manufacturer can maximize profit by optimizing the production quantities of its products. In this case, the manufacturer produces skateboards and in-line skates, with a constraint on the daily production capacity for each product. By determining the optimal quantities of skateboards and in-line skates to produce, the company can achieve the highest profit possible.

The key to maximizing profit lies in finding the balance between the production capacities, demand from dealers, and profitability of each product. In this scenario, the profit on each skateboard is $12, while the profit on each pair of in-line skates is $18. By formulating a system of inequalities based on the production capacities and dealer demands, the manufacturer can identify the feasible region for production quantities.

Using linear programming techniques, the company can graph the feasible region and evaluate the profit function at the corner points to determine the maximum profit. In this case, the corner points represent different combinations of skateboards and in-line skates that adhere to the constraints.

After evaluating the profit function at each corner point, the manufacturer can identify the production quantities that yield the highest profit. By producing 60 skateboards and 30 pairs of in-line skates per day, the company can achieve a maximum profit of $1800. This optimization strategy allows the manufacturer to make the most efficient use of its resources and meet the demands of its dealers while maximizing profitability.

By implementing effective production planning and optimization strategies, sporting goods manufacturers can enhance their financial performance and competitiveness in the market. Understanding the relationship between production quantities, demand, and profitability is essential for achieving long-term success in the industry.