Answer to Question #194521 in Operations Research for Stephanie

Question

This pandemic, Abheedette learned to bake while on home quarantine. She

also realized that she will be able to make P60.00 profit per tray of banana muffins and

P120.00 profit per tray of blueberry muffins. She needs 2 cups of milk and 3 cups of flour

to bake a tray of banana muffins. And, baking a tray of blueberry muffins takes 4 cups

of milk and 3 cups of flour. She has 16 cups of milk and 15 cups of flour. How many trays

of each flavor must be baked to maximize the profit?

a. Define the variable used

b. LP Model

c. Identify the feasible region

d Corner Points and the objective functions

e. Optimal Solution (final answer)

Answer 1

Givan That

profit per tray of banana muffins = P60

profit per tray blueberry muffins = P120

a)

let x be the banana muffins and

y be the blueberry muffins

b)

$2x + 4y \le 16 \\ 3x+34 \le 15 \\ x\ge 0 , y\ge 0\\$

c)

d)

therefore point of intersection

x+2y=8

x+y=5

now x= 2 and y=3

hence (2,3) is point of intersection ,

so the corner points are given as

(0,0) , (0,4) , (0,5) , (2,3) , (5,0) , and (8,0)

and objective function is

Max Z = P60x + P120y

e)

$\def\arraystretch{1.5} \begin{array}{c:c:c} x & y & Max Z = P60x + P120y \\ \hline 0 & 0 & 0P \\ \hdashline 0 & 4 & 480P \\ \hdashline 0 & 5 & 600P ..........max \\ \hdashline 2 & 3 & 480P \\ \hdashline 5 & 0 & 300P \\ \hdashline 8 & 0 & 480P \end{array}$

hence for maximum profit we need to x =0 banana muffins and y=5 tray of bluberry muffins