NEED ANSWER ASAP, I WILL GIVE YOU THUMBS UP!

Hopping Gnome Brewing Company produces several different types of beer each year. There are a limited amount of grains and hops available each year for purchase to make the beer in 4500-pint batches. There is various demand for each type of beer produced. Hopping Gnome wants to try to maximize the profit while meeting the conditions listed below. The following information is given:

	Light	Golden	Heavy	Light	Dark	Heavy		Cost per
	Brew	Brew	Wheat	Wheat	Ale	Stout	Availability	(lb, hr, etc)
Percent of Demand	28 - 33	20 - 25	15 - 25	8 - 13	10 - 15	5 - 10
2-Row Grain (lb)	600	500	475	500	550	475	30,000	$0.45
6-Row Grain (lb)	120	100	150	130	200	250	8,500	$0.38
Crystal Grain (lb)	130	50	40		100		4,000	$0.40
Vienna Grain (lb)		150	250	200	60		5,500	$0.41
Barley (lb)	100		125	125		100	5,000	$0.43
Malt Extract (lb)	40	10	50	40	30	20	2,500	$0.35
Hallertauer Hops (lb)	10	15	12	11			600	$0.34
Kent Goldings Hops (lb)			3		10	10	300	$0.31
Tettnanger Hops (lb)	14		12	12	14	12	600	$0.35
Labor (hr)	80	60	70	85	75	90	4,000	$22.00
Average # pints per batch	4,500	4,500	4,500	4,500	4,500	4,500
Beer price (per pint)	$3.50	$3.45	$3.00	$3.75	$4.10	$3.20

There are also overhead costs of $8000 per batch of beer.

Managerial Report

Determine how much batches of each beer Hopping Gnome should produce while meeting demands and maximizing profit. Your report should include the following:

1. Calculate the profit function per batch of each beer. Be sure to consider the costs of each ingredient used and labor costs.
2. Develop and solve an LP model that will help determine how many batches Hopping Gnome should make of each product to prepare for the next year. Be sure to define your decision variables and write out your objective function and all of your constraints.
3. In the brewing business, the price and availability of ingredients can vary a lot. Examine the effect of a 10 percent decrease in the availability of all of the ingredients on the optimal solution (so your supply of ingredients in 10% less for each one).
4. Due to a small demand in Heavy Stout beer, Hopping Gnome would like to know what would happen if it was removed from production. Remove Heavy Stout Beer from the model and solve the model again. What are the new objective function, constraints, and results? Modify your model from part b. How much difference is there from your answer in part a concerning how many batches to produce of each? How much does it affect profits? Do you recommend removing heavy stout from production? Support your answer with mathematical as well as logical evidence.