Hi! There are three problems that have to be completed for this assignment. It relates to math & information systems. Due date is 4/19/16 at 5:00 pm New York Eastern Time. Any questions or extra info (ex. course powerpoints) I can provide, please message if needed. Thanks in advance!

**Problem 2**: (30 pts) A large bakery opens 365 days per year and buys flour in 25-pound bags. The bakery uses an average of 48,600 bags a year. Preparing an order and receiving a shipment of flour involves a cost of $100 per order. Monthly carrying costs are $1 per bag.

a. (5 pts) Determine the economic order quantity.

Suppose that the economic order quantity that you calculate in Part 1 is used to order by the bakery, answer the following questions:

b. (5 pts) What is the average number of bags on hand?

c. (5 pts) How many orders per year will there be?

d. (5 pts) Compute the total cost of ordering and carrying flour.

e. (5 pts) The bakery’s flour delivery lead time is 3 days. What is their re-order point?

Suppose due to warehouse capacity issues, the bakery can only hold a maximum of 500 bags of flour at any given time:

f. (5 pts) How much more do they have to pay for inventory costs compared to when they can order the EOQ?

**Problem 3**: (40 pts) Teddy Bower is an outdoor clothing and accessories chain that purchases a line of parkas at $10 each from its Asian supplier, TeddySports. Unfortunately, at the time of order placement, demand is still uncertain. Teddy Bower forecasts that its demand is normally distributed with mean of 2,100 and standard deviation of 1,200. Teddy Bower sells these parkas at $22 each. Unsold parkas have little salvage value; Teddy bower simply gives them away to a charity.

a. (5 pts) What is the probability that the demand of the parka is greater than 1,800 units?

b. (5 pts) What is the probability that the demand of the parka is between 1,800 and 2,500 units?

c. (5 pts) How many parkas should Teddy Bower buy from TeddySports to maximize expected profit?

d. (5 pts) If Teddy Bower wishes to ensure a 98.5 percent in-stock probability, how many parkas should it order?

For parts e and f, assume Teddy Bower orders 3,000 parkas.

e. (10 pts) Evaluate Teddy Bower’s expected profit.

f. (5 pts) Evaluate Teddy Bower’s stockout probability.

g. (5 pts) TeddySports approaches Teddy Bower with a new offer: with a 30% premium, Teddy Bower may place a second order during their selling season and TeddySports will ship the order by air so that Teddy Bower will receive it in time to satisfy any remaining demand during the regular selling season. Given this new offer, how many parkas should Teddy Bower buy from TeddySports in their first order in order to maximize expected profit?

**Problem 4**: (45 pts) Flextrola, Inc., an electronics systems integrator, is planning to design a key component for their next-generation product with Solectrics. Flextrola will integrate the component with some software and then sell it to consumers. Given the short life cycles of such products and the long lead times quoted by Solectrics, Flextrola only has one opportunity to place an order with Solectrics prior to the beginning of its selling season. Flextrola’s demand during the season is normally distributed with a mean of 1,000 and a standard deviation of 600.

Solectrics’ production cost for the component is $52 per unit and it plans to sell the component for $72 per unit to Flextrola. Flextrola incurs essentially no cost associated with the software integration and handling of each unit. Flextrola sells these units to consumers for $121 each. Flextrola can sell unsold inventory at the end of the season in a secondary electronics market for $50 each. The existing contract specifies that once Flextrola places the order, no changes are allowed to it. Also, Solectrics does not accept any returns of unsold inventory, so Flextrola must dispose of excess inventory in the secondary market.

a. (5 pts) What is the probability that Flextrola’s demand is between 800 and 1,200 units?

b. (5 pts) Under this contract, how many units should Flextrola order to maximize its expected profit?

c. (10 pts) What is Flextrola’s expected profit when the order quantity calculated in Part (b) is ordered?

d. For Parts (d) through (h), assume Flextrola orders 1,200 units.

e. (5 pts) What are Flextrola’s expected sales?

f. (5 pts) How many units of inventory can Flextrola expect to sell in the secondary electronics market?

g. (5 pts) What is Flextrola’s expected profit?

h. (5 pts) What is Solectrics’ expected profit?

i. (5 pts) What is Flextrola’s stockout probability?

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