A renowned chocolatier, Francesco Schreder, makes three kinds of chocolate confectionery: artisanal truffles, handcrafted chocolate nuggets, and premium gourmet chocolate bars. He uses the highest quality of cacao butter, dairy cream, and honey as the main ingredients. Francesco makes his chocolates each morning, and they are usually sold out by the early afternoon.

For a pound of artisanal truffles, Francesco uses 1 cup of cacao butter, 1 cup of honey, and 1/2 cup of cream. The handcrafted nuggets are milk chocolate and take 1/2 cup of cacao, 2/3 cup of honey, and 2/3 cup of cream for each pound. Each pound of the chocolate bars uses 1 cup of cacao butter, 1/2 cup of honey, and 1/2 cup of cream. One pound of truffles, nuggets, and chocolate bars can be purchased for $35, $25, and $20, respectively. A local store places a daily order of 10 pounds of chocolate nuggets, which means that Francesco needs to make at least 10 pounds of the chocolate nuggets each day. Before sunrise each day, Francesco receives a delivery of 50 cups of cacao butter, 50 cups of honey, and 30 cups of dairy cream.

Formulate and solve the LP model that maximizes revenue given the constraints. How much of each chocolate product should Francesco make each morning? What is the maximum daily revenue that he can make?

How many pounds of chocolate truffles should Francesco make? _________

How many pounds of chocolate nuggets should Francesco make? _________

How many pounds of chocolate bars should Francesco make? __________

Maximum daily revenue _________

Report the shadow price and the range of feasibility of each binding constraint.

Note: If the answer to constraints is "Binding" enter "Shadow price" and "Range of feasibility"

Shadow Price Range of Feasibility

From To

Cacao Butter Constraint ___________ ___________ ______ ______

Honey Constraint ___________ ___________ ______ ______

Cream Constraint ___________ ___________ ______ ______

Chocolate Nugget Constraint ___________ ___________ ______ ______

If the local store increases the daily order to 25 pounds of chocolate nuggets, how much of each product should Francesco make?

How many pounds of chocolate truffles should Francesco make? _________

How many pounds of chocolate nuggets should Francesco make? _________

How many pounds of chocolate bars should Francesco make? __________

Maximum daily revenue _________