A major snack company produces a variety of cakes and cookies that are sold in various grocery stores and online stores. One of the famous products of this company is "dark chocolate delight", which is a snack cake. The cakes are individually packed and sold in boxes of dozens. The machinery used to produce this product is 20 years old. Over time, the variation in the weight of cakes produced gradually increased. The weight of the individual cake is listed as 50 grams and the actual weight follows a normal distribution with a mean of 56 grams and a standard deviation of 2 grams. The production process is set at 56 grams to limit the percentage of cakes that are underweight. As we know increased variation will result in increased waste. The ingredients cost about $ 0.0032 per gram of cake. The company currently produces 24,000 "dark chocolate cakes" (that is 2000 boxes of dozen cakes) each day and makes a profit of $ 0.50 per box sold.

The company is considering replacing existing machinery with new equipment, which will increase the daily production rate by 25%. With the new equipment, the standard deviation of cake weight would be 1.6 grams. Senior marketing leaders are convinced that the demand for "dark chocolate delight" is very high and selling more boxes would not be a problem. The cost of new machinery including installation is $ 500,000.

As a team reporting to the CFO of the company, which option you would recommend (staying with old equipment or buying new equipment). Please justify your decision with statistical analysis.