Question 1033319: Baking a tray of blueberry muffins takes 4 cups of milk and 3 cups of flour. A tray of banana muffins takes 2 cups of milk and 3 cups of flour. A baker has 16 cups of milk and 15 cups of flour. Write a system of equations representing this situation. Solve the system of equations.
Use the following information to determine the number of trays of banana muffins to maximize the profit.
You will make $3 profit per tray of blueberry muffins and $2 profit per tray of banana muffins.
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! Baking a tray of blueberry muffins takes 4 cups of milk and 3 cups of flour. A tray of banana muffins takes 2 cups of milk and 3 cups of flour.
A baker has 16 cups of milk and 15 cups of flour.
Write a system of equations representing this situation. Solve the system of equations.
Use the following information to determine the number of trays of banana muffins to maximize the profit.
You will make $3 profit per tray of blueberry muffins and $2 profit per tray of banana muffins.
-----
-------------------------
Milk function:: 4u + 2n <= 16
Flour function: 3u + 3n <= 15
--------------------
Graph:: u <= -(1/2)n + 4
Graph:: u <= -n + 5
-------------------------
-------------------------
Find the point of intersection::
-(1/2)n + 4 = -n + 5
(1/2)n = 1
If n = 2; then u = 3
-----
(n,u) Vertices:: (0,4),(5,0),(2,3)
---------
Evaluate Profit at the vertices::
Profit function:: P = 2n + 3u
(0,4) gives P = 2*0 + 3*4 = 12
(5,0) gives P = 2*5 + 3*0 = 10
(2,3) gives P = 2*2 + 3*4 = 16
------
Max Profit comes with 2 banana and 3 blueberry
---------------
Cheers,
Stan H.
|
|
|
