The answer to this question would be 40$
The objective function of a linear programming problem is a linear function.
A valid objective function is (b) Min 4x+3y+(2/3)z
The form of the objective function of a linear programming problem is:

The above function means that:
- The objective function cannot contain the product of the variables
- The objective function cannot contain the quotient of the variables
The above highlights mean that:
- The objective function can contain the sum of the variables
- The objective function can contain the difference of the variables
Hence, the valid objective function is (b) Min 4x+3y+(2/3)z
Read more about objective functions at:
brainly.com/question/11206462
Answer:
Numbers of students at a primary school before= 240
Number of increased students =42
Again,
Increased number of students in percent(%)= 42/240×100%= 17.5%
Therefore 17.5% students are increased this year.
Answer:
Using either method, we obtain: 
Step-by-step explanation:
a) By evaluating the integral:
![\frac{d}{dt} \int\limits^t_0 {\sqrt[8]{u^3} } \, du](https://tex.z-dn.net/?f=%5Cfrac%7Bd%7D%7Bdt%7D%20%5Cint%5Climits%5Et_0%20%7B%5Csqrt%5B8%5D%7Bu%5E3%7D%20%7D%20%5C%2C%20du)
The integral itself can be evaluated by writing the root and exponent of the variable u as: ![\sqrt[8]{u^3} =u^{\frac{3}{8}](https://tex.z-dn.net/?f=%5Csqrt%5B8%5D%7Bu%5E3%7D%20%3Du%5E%7B%5Cfrac%7B3%7D%7B8%7D)
Then, an antiderivative of this is: 
which evaluated between the limits of integration gives:

and now the derivative of this expression with respect to "t" is:

b) by differentiating the integral directly: We use Part 1 of the Fundamental Theorem of Calculus which states:
"If f is continuous on [a,b] then

is continuous on [a,b], differentiable on (a,b) and 
Since this this function
is continuous starting at zero, and differentiable on values larger than zero, then we can apply the theorem. That means:
