Instructions:

For this question, you must submit one of the numerical answers below.

The solution to this question will be graded. You must submit the solution in the Assignment $1$ accompanying PDF file.

To receive points, you must submit the solutions of Assignment $1$ in the accompanying file. $.$

Question:

You are in charge of marketing a new pair of sunglasses: The Ray Bob. For a sales cycle, it costs a base amount of $70,000$$$,$ and then $20$$ for each pair of glasses produced. When you set the price at $300$$ for a pair, you sell $5,000$ pairs. If you increase the price by $2$$$,$ you sell $14$ fewer pairs. Let x be the number of pairs of glasses produced.

Model the function C$($x$),$ the production cost.

Model the function p$($x$),$ the price per pair of glasses.

Model the function R$($x$),$ the revenue from production.

Model the function P$($x$),$ the profit from production.

Find the value of x that maximizes the profit.

Calculate P$($x$),$ the maximum profit. Submit the answer below.

Note: Your answer must be written in decimal form with EXACTLY $2$ decimal places of precision.

Your Answer: