The Green Leaf Bakery Makes Two Types of Chocolate Cakes $p ( x , y ) = 151 x - 0.2 x ^ { 2 } + 200 y - 0.1 y ^ { 2 }$

question 58

Essay

The Green Leaf Bakery makes two types of chocolate cakes, Delicious and Extra Delicious.Each Delicious requires 0.1 lb of European chocolate, while each Extra Delicious requires 0.2 lb.Currently there are only 233 lb of chocolate available each month.Suppose the profit function is given by: $p ( x , y ) = 151 x - 0.2 x ^ { 2 } + 200 y - 0.1 y ^ { 2 }$ where x is the number of Delicious cakes and y is the number of Extra Delicious cakes that the bakery produces each month.
(a)How many of each cake should the bakery produce each month to maximize profit?
(b)What is the value of $\lambda$ in part (a)(if $\nabla p = \lambda \nabla g$ )? What does it mean?
(c)It will cost $19.00 to get an extra pound of European chocolate.Should the bakery buy it?

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Definitions:

Net Promoter Score

A metric used to gauge the loyalty of a firm's customer relationships, based on how likely customers are to recommend the company to a friend or colleague.

Customer Satisfaction

The measure of how well a company's products or services meet or surpass the expectations of its customers.

Long-Term Customer Relationship

An ongoing engagement between a business and its customers aimed at fostering loyalty, trust, and sustained interaction over time.

Short-Term Customer Relationship

A business strategy focusing on quick and immediate sales with little emphasis on building long-term customer loyalty.