PLEASE SHOW EACH STEP 1. Inventory management. a) Lakeside Bakery bakes fresh croissants every morning. Assume the demand approximately follows a normal distribution.

The true demand mean of the demand data = 178.9 The standard deviation of the demand data = 32.25

Each croissant costs the bakery $6.75 to make and is sold for $18. Unsold croissants at the end of the day are purchased by a nearby nursing home for $1 each. Assume no goodwill cost. What optimal service level (critical ratio) balances the underage and overage costs? How many croissants should the company bake each day to maximize its expected profit? [Note: Keep four decimal places for calculating the critical ratio and the Z value. Round the final order quantity to an integer.]

b) The weekly demand for a product

The true demand mean of the demand data = 240.6 The standard deviation of the demand data = 20.26

The fixed cost to place an order is $600, and the lead time from ordering to receipt is 2 weeks. The weekly inventory carrying cost is $0.1 per unit. The operations manager decides to use a fixed-order quantity inventory control policy. What is the optimal order quantity? How frequently will the firm order? What is the corresponding reorder point if the firm wants to make stockout occur with no more than a 5% chance during the lead time? [Note: Keep two decimal places for every step of the calculation and your answers.]

PLEASE SHOW EACH STEP. I would highly appreciate it. Thank you.