Ishaan and his friends have 40$ to spend at a restaurant.
1 answer:
The number of salads Ishaan and his friends can afford is 6 salads.
<h3>What are Word Problems?</h3>
Word Problems in mathematics involve crucial understanding and the use of variables and arithmetic operations to solve real-life cases.
From the given information;
- The total amount with Ishaan and his friends = $40
- If they decided to spend the money on salad(x) and one salad(x) cost = $6
Thus, the number of salads they can purchase is:
x = 6 salads remaining $4
Therefore, we can conclude that the number of salads they can purchase with $40 is 6 salads with a remaining amount of $4.
Learn more about word problems here:
You might be interested in
Answer:
<em>Maximum value of f=2.41</em>
Step-by-step explanation:
<u>Lagrange Multipliers</u>
It's a method to optimize (maximize or minimize) functions of more than one variable subject to equality restrictions.
Given a function of three variables f(x,y,z) and a restriction in the form of an equality g(x,y,z)=0, then we are interested in finding the values of x,y,z where both gradients are parallel, i.e.
for some scalar called the Lagrange multiplier.
For more than one restriction, say g(x,y,z)=0 and h(x,y,z)=0, the Lagrange condition is
The gradient of f is
Considering each variable as independent we have three equations right from the Lagrange condition, plus one for each restriction, to form a 5x5 system of equations in .
We have
Let's compute the partial derivatives
The Lagrange condition leads to
Operating and simplifying
Replacing the value of in the two first equations, we get
From the first equation
Replacing into the second
Or, equivalently
Squaring
To solve, we use the restriction h
Multiplying by 100
Replacing the above condition
Solving for x
We compute the values of y by solving
For
And for
Finally, we get z using the other restriction
Or:
The first solution yields to
And the second solution gives us
Complete first solution:
Replacing into f, we get
f(x,y,z)=-0.4
Complete second solution:
Replacing into f, we get
f(x,y,z)=2.4
The second solution maximizes f to 2.4