3. A 3D printing machine company is currently selling printers at a price of $900. It costs $600 to make one printer and they currently sell 9000 per month in each of 5 similar markets. Based on previous research, they have found that dropping the price initially increases the units sold at a rate of 70 per dollar but this eect tapers o completely when the price reaches $200. Normally, they also spend $50000 on advertising in each market. However, in the last year, they have increased the advertising budget by $5000 in one test market and noticed the following sales figures over 12 months.

Month	Sales
Jan	9040
Feb	9070
Mar	9030
April	9080
May	9090
June	9120
July	9130
Aug	9075
Sept	9140
Oct	9170
Nov	9220
Dec	9240

A. Assume that these sales numbers are not from an approximately normal distribution, and assume that the com- pany will not spend more than $90000 on advertising in any market. Find a reasonable range of optimal price, advertising budget, and maximum profit. B. What is the worst possible benefit from raising the advertising limit by another $100?

C. What is the highest reasonable sensitivity of optimal price, advertising budget, and maximum profit to the 70 per dollar rate given above? D. (This is unrelated to A,B,C) Make a prediction interval for NEXT January sales in the test market. Comment on the fit of your prediction model to the data and the uncertainty due to your sample.