Lakeside bakery bakes fresh pies every morning. The daily demand for its apple pies are normally distributed with a mean of 50 and standard deviation of 10. Each apple pie costs the the bakery $6.75 to make and is sold for $17.99. Unsold pies at the end of the day are purchased by a nearby soup kitchen for 99 cents each. Based on the demand distribution how many apple pies should the company bake each day to maximize its profit? Show all steps of the analysis.