How to Determine the Number of Accessories to Produce for Maximum Profit?
How many accessories produced yield a similar profit for the company?
We need to write an algebraic equation $y = (100 - 10x^2)x - 10x$ where $y$ represents the profit and $x$ represents the number of accessories produced in millions.
I used $10$ because that's the cost of making each accessory. $100 - x^2 = \text{consumer price}$. $x - 10x = \text{accessory-cost to make all the accessories}$.
We know that $2$ million accessories make $100$ million. So, the number of accessories that make $100$ should be around $2$ million. In the options, the $1.45$ is given which is close to $2$.
The other number of accessories that produced yields the same profit is 1. 45 million.
To determine the number of accessories to produce for maximum profit, we need to consider the cost of producing each accessory and the selling price. In this case, the company charges $100 - 10x^2$ for each accessory, where $x$ is the number of accessories produced in millions. It costs the company $10 to make each accessory, which means the total cost to make all the accessories would be $10x$.
The profit can be calculated using the formula $y = (100 - 10x^2)x - 10x$. By substituting $2$ million for $x$ (as the company currently produces $2$ million accessories and makes a profit of $100$ million), we can determine the profit.
To find the number of accessories that yield a similar profit, we can set the profit equal to $100$ and solve for $x$. The other number of accessories that yields the same profit is $45$ million, which is close to the initial production of $2$ million.