Question

Help!I am stuck so a step by step explaination would really help :)

Answer 1

Let x represent the number of trees of corn muffins

Let y represent the number of trees of bran muffins

$\begin{gathered} 4x\text{ + 2y }\leq\text{ 16} \\ 3x\text{ + 3y }\leq15 \\ \end{gathered}$

Then reducing it to the simplest form

$\begin{gathered} 2x\text{ + y }\leq\text{ 8} \\ x\text{ + y }\leq5 \\ \end{gathered}$

Then the number of corn muffins with bran muffins to make a profit

$3x\text{ + 2y}$

where

$x\text{ }\ge\text{ 0 , y}\ge\text{ 0 }$

The graph showing all points of x and y values to be tested to obtain the maximum profit is given below

$\begin{gathered} \text{GIven the following points} \\ (3,2),(0,5),(4,0)\text{ and (0,0)} \end{gathered}$$\begin{gathered} \text{The Profit formula will be} \\ P=3x+2y \end{gathered}$$\begin{gathered} \text{Substitute the coordinates points to obtain the maximum profit} \\ \text{For (3,2)} \\ x=3.y=2 \\ P=3(3)+2(2)=9+4=\text{ \ 13} \\ \text{For (0 , 5)} \\ x=0,y=5 \\ P=3(0)+2(5)=0+10=\text{ \ 10} \\ For\text{ (4 , 0)} \\ x=4,y=0 \\ P=3(4)+2(0)=12+0=\text{ \ 12} \end{gathered}$

From the above test, the points that yield the maximum profit is at ( 3, 2), therefore we can conclude that the baker would need 3 trays of corn muffins and 2 trays of bran muffins to maximize his profit

The answer is 3 trays of corn muffins and 2 trays of bran muffins