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Answer:
1) The system of inequalities are;
x × 1.25 + y × 1.5 ≥ 24
x + y ≤ 10
Please find attached the required graph of the two inequalities ,created with Microsoft Excel
2) The graph of inequality shows that Larissa cannot to make less than 10 loafs of bread and sell them for over $24 at the given prices of each loaf of bread
Step-by-step explanation:
1) The maximum number of loaves Larissa plans to make = 10
The price at which she sells each of x loaves of banana bread = $1.25
The price at which she sells each of y loaves of nut bread = $1.50
The total amount she hopes to make = $24
The system of inequalities are;
x × 1.25 + y × 1.5 ≥ 24
x + y ≤ 10
Making y the subject of both inequalities gives;
For the first inequality, we have,
y ≥ 24/1.5 - 1.25/1.5·x which gives;
y ≥ 16 - 5/6·x
For the second inequality, we have,
y ≤ 10 - x
Please find attached the required graph of the two inequalities
2) From the attached graph of inequality, created with Microsoft Excel, it shows that it is not possible for Larissa to make less than 10 loafs of bread and at the same time sell them for over $24 if the price of each banana bread is $1.25 and the price of each nut bread is $1.50.
Given:
and,
K = 1
We would require to do the synthetic division of the above problem in order to know whether K=1 is a lower bound or not. Let's do it!
Steps of Synthetic Division:
1. Write the coefficients of the equation, and before that write 1. Like,
1 ║ 4 -2 2 4
As you can see, the coefficients of the equation are seperated by ║.
2. Drop down the first value after ║as it is. Like:
1 ║ 4 -2 2 4
:
----------------------
4
3. Multiply 4 with 1 and then place the resultant value under -2 and then add that resultant value with -2. Like
1 ║ 4 -2 2 4
: 4
----------------------
4 2
4. Repeat Step 3 until you're done.
1 ║ 4 -2 2 4
: 4 2
----------------------
4 2 4
1 ║ 4 -2 2 4
: 4 2 4
----------------------
4 2 4 8
Now every value, +4, +2, +4, +8, under the bar(---------) is positive; therefore, it means that K=1 is the upper bound, NOT lower bound.
Ans: K=1 is NOT a lower bound.
-i
and,
K = 1
We would require to do the synthetic division of the above problem in order to know whether K=1 is a lower bound or not. Let's do it!
Steps of Synthetic Division:
1. Write the coefficients of the equation, and before that write 1. Like,
1 ║ 4 -2 2 4
As you can see, the coefficients of the equation are seperated by ║.
2. Drop down the first value after ║as it is. Like:
1 ║ 4 -2 2 4
:
----------------------
4
3. Multiply 4 with 1 and then place the resultant value under -2 and then add that resultant value with -2. Like
1 ║ 4 -2 2 4
: 4
----------------------
4 2
4. Repeat Step 3 until you're done.
1 ║ 4 -2 2 4
: 4 2
----------------------
4 2 4
1 ║ 4 -2 2 4
: 4 2 4
----------------------
4 2 4 8
Now every value, +4, +2, +4, +8, under the bar(---------) is positive; therefore, it means that K=1 is the upper bound, NOT lower bound.
Ans: K=1 is NOT a lower bound.
-i