Lake Grove Confectionaries (LGC) sells chocolates for the holiday season in specially designed boxes. The firm sells four designs, and currently all packaging is done in the plant as chocolates are manufactured. All manufacturing and packaging for the holiday season are completed before the start of the season. The demand forecast for each of the four designs is normally distributed, with a mean of 20,000 and a standard deviation of 8,000. Each box costs $10 and is sold for $20. Any unsold boxes at the end of the season are discounted to $8, and they all sell out at this price. The cost of holding a box in inventory for the entire season before selling it at a discount is $1. a. How many boxes of each design should LGC manufacture? b. What is the expected profit from this policy? c. How many boxes does LGC expect to sell at a discount? d. An option being considered by LGC is to separate chocolate production from packaging. Chocolates will be produced before the start of the season, but packaging will be done on an express line as orders come in. The express line and separation of steps adds $2 to the cost of production. How many boxes of chocolates should LGC manufacture if it decides to postpone packaging? What is the expected profit? How many boxes will LGC sell at a discount if it uses postponement?