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You are the purchasing manager of a bakery that operates on the local level. You produce four types of products: scones which earn $1 revenue, bagels which earn $2 revenue, donuts which earn $0.25 revenue, and cookies which earn $0.75 revenue.
A scone requires 0.05 lbs butter, 0.2 lbs flour, 0.25 eggs, 0.1 lbs sugar, and 0.02 gallons of milk. A bagel requires 0.15 lbs butter, 0.25 lbs flour, 0.1 eggs, 0.05 lbs sugar, and 0.01 gallons of milk. A donut requires 0.05 lbs butter, 0.08 lbs flour, 0.2 eggs, 0.15 lbs sugar, and 0.15 gallons of milk. A cookie requires 0.15 lbs butter, 0.3 lbs flour, 0.05 eggs, 0.12 lbs sugar, and 0.05 gallons of milk.
To have enough items on display and to keep the bakers busy, you must produce at least 100 of each. However, since these are perishable goods, we seldom manage to sell more than 500 of each before the remainder go bad, so don’t make more than 500 of any item. Because of past demand patterns, you should make 2 donuts for each bagel and 3 cookies for each scone. You have 130 lbs of butter. You have 300 lbs of flour. You have 180 eggs. You have 160 lbs of sugar. You have 100 gallons of milk.
Questions: What is the objective function value? What is the maximum revenue that you can earn on a scone that will not result in a change in the product mix? How many donuts do you make? How much sugar is left over? What is the benefit of having another dozen eggs?
do provide explanations for every step...
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