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

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?