Please show all the work
Question 1
A manufacturer produces umbrellas with the followingparameters:
The monthly demand for umbrellas is 3000
Daily usage is 100 (assume 1 month = 30 days and demand isuniform throughout the month)
The production rate is 400 per day
Setup cost is $200 for a run
Holding cost is $1 per umbrella per month
What is the economic production quantity?
Question 2
Suppose a gas station has expected sales of 6000 gallons duringlead time. Sales are normally distributed with a standard deviationof 400 gallons.
To avoid stockouts with probability P(z < +3.00), what shouldbe the reorder point?
Question 3
Suppose a gas station has daily sales of 1500. Expected leadtime is four days, normally distributed with a standard deviationof one day.
To avoid stockouts with probability P(z < +3.00), what shouldbe the reorder point?
Question 4
Suppose a gas station has expected daily sales of 1500 gallons,normally distributed with a standard deviation of 400 gallons.Expected lead time is four days, normally distributed with astandard deviation of one day.
To avoid stockouts with probability P(z < +3.00), what shouldbe the reorder point?
Question 5
Suppose a gas station has daily sales of 1500. Lead time is fourdays and orders are placed every Monday to arrive on Fridays.
What should the order quantities be if:
Safety stock and on-hand inventory at the time of ordering arezero?
Safety stock is 1000 gallons and on-hand inventory at the timeof ordering is 3000 gallons?
Safety stock is 3000 gallons and on-hand inventory at the timeof ordering is also 3000 gallons?
Question 6
A grocery store sells fresh cookies, which are only sold for oneday. Any unsold cookies are donated to charity for a taxdeduction:
Unit revenue is $1.00
Unit cost is $0.50
Unit salvage value is $0.20
What is the optimal service level?
Assume demand is normally distributed with mean = 200 andstandard deviation = 25, and the z-score for the optimal servicelevel was approximated as 0.3, what is the optimal stockinglevel?
