# Profit Maximization and Marginal Cost Analysis for Ajax Cleaning Products

## What is the marginal cost (MC) curve for Ajax?

Given Ajax's pricing strategy, what is the profit-maximizing level of output for Ajax?

## Marginal Cost (MC) Curve for Ajax:

The marginal cost (MC) curve for Ajax can be found by taking the derivative of the total cost (TC) equation with respect to quantity (Q). The TC equation given is TC = 800,000 - 5,000Q + 25Q^2.

To find the MC curve, we differentiate the TC equation with respect to Q: MC = dTC/dQ. Differentiating the equation gives us MC = -5,000 + 50Q. So, the marginal cost (MC) curve for Ajax is -5,000 + 50Q.

## Profit-Maximizing Level of Output for Ajax:

To find the profit-maximizing level of output for Ajax, we need to find where marginal cost (MC) equals marginal revenue (MR). Since Ajax is charging the same price as Tile King ($20,000), the marginal revenue is also $20,000. Setting MC = MR, we have -5,000 + 50Q = 20,000. Solving for Q, we get Q = 300. Therefore, the profit-maximizing level of output for Ajax is 300 units.

To find Ajax's total dollar profit at this output level, we substitute Q = 300 into the TC equation: TC = 800,000 - 5,000(300) + 25(300^2). Calculating this gives us TC = 7,550,000. Therefore, Ajax's total dollar profit at this output level is $7,550,000.

Reflecting on the analysis above, it is evident that Ajax Cleaning Products has a well-defined strategy in place to maximize its profit in a competitive market. By setting the same price as the industry leader, Tile King, Ajax aims to avoid a price war and focus on optimizing its output level.

The calculation of the marginal cost (MC) curve for Ajax provides valuable insights into the cost structure of the firm. With a linear relationship between quantity produced and marginal cost, Ajax can make informed decisions about production levels and pricing strategies.

Furthermore, the determination of the profit-maximizing level of output showcases Ajax's commitment to financial success. By balancing marginal cost and marginal revenue, Ajax can achieve optimal profitability at 300 units of output, leading to a total dollar profit of $7,550,000.

In conclusion, the strategic pricing approach and detailed cost analysis demonstrate Ajax Cleaning Products' ability to thrive in a competitive industry landscape. By leveraging data-driven decision-making, Ajax can position itself for sustained growth and profitability in the market.