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?

Distinguish between substitutes and complements.

Apply the concepts of the substitution effect and income effect.

Analyze and interpret demand curves and how they are derived.

Understand the relationship between income levels and consumer preferences.

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