# Fill in the blank/s: A system of linear inequalities is used to represent restrictions, or ________ on a function that must be maximised or minim,ised. Use the graph of such a system of inequalities, the maximum and minimum values of the function occur at one or more of the _____________ points.

Question
Fill in the blank/s: A system of linear inequalities is used to represent restrictions, or ________ on a function that must be maximised or minim,ised. Use the graph of such a system of inequalities, the maximum and minimum values of the function occur at one or more of the _____________ points.

2021-01-05
1) The calculus helps in understanding the changes between values that are related by a function. It is used in different areas such as physics, biology and sociology and so on. The calculus is the language of engineers, scientists and economics.
2) Linear programming is a method for solving problems in which a particular quality that must be maximized or minimized is limited other factors. An objective function is an algebraic expression in two or more variables describing a quality that must be maximized.

### Relevant Questions

4.7 A multiprocessor with eight processors has 20attached tape drives. There is a large number of jobs submitted tothe system that each require a maximum of four tape drives tocomplete execution. Assume that each job starts running with onlythree tape drives for a long period before requiring the fourthtape drive for a short period toward the end of its operation. Alsoassume an endless supply of such jobs.
a) Assume the scheduler in the OS will not start a job unlessthere are four tape drives available. When a job is started, fourdrives are assigned immediately and are not released until the jobfinishes. What is the maximum number of jobs that can be inprogress at once? What is the maximum and minimum number of tapedrives that may be left idle as a result of this policy?
b) Suggest an alternative policy to improve tape driveutilization and at the same time avoid system deadlock. What is themaximum number of jobs that can be in progress at once? What arethe bounds on the number of idling tape drives?
An objective function and a system of linear inequalities representing constraints are given.
a. Graph the system of inequalities representing the constraints.
b. Find the value of the objective function at each corner of the graphed region.
c. Use the values in part (b) to determine the maximum value of the objective function and the values of x and y for which the maximum occurs.
$$\displaystyle{z}={2}{x}+{3}{y}$$
$$\displaystyle{\left\lbrace\begin{array}{c} {x}{\quad\text{and}\quad}{y}\ge{0}\\{2}{x}+{y}\le{8}\\{2}{x}+{3}{y}\le{12}\end{array}\right.}$$

find the values of b such that the function has the given maximum or minimum value. $$f(x) = -x^2+bx-75$$, Maximum value: 25

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Consider the curves in the first quadrant that have equationsy=Aexp(7x), where A is a positive constant. Different valuesof A give different curves. The curves form a family,F. Let P=(6,6). Let C be the number of the family Fthat goes through P.
A. Let y=f(x) be the equation of C. Find f(x).
B. Find the slope at P of the tangent to C.
C. A curve D is a perpendicular to C at P. What is the slope of thetangent to D at the point P?
D. Give a formula g(y) for the slope at (x,y) of the member of Fthat goes through (x,y). The formula should not involve A orx.
E. A curve which at each of its points is perpendicular to themember of the family F that goes through that point is called anorthogonal trajectory of F. Each orthogonal trajectory to Fsatisfies the differential equation dy/dx = -1/g(y), where g(y) isthe answer to part D.
Find a function of h(y) such that x=h(y) is the equation of theorthogonal trajectory to F that passes through the point P.
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A nylon thread is to be subjected to a 2.5-lb tensile load. Knowing that $$\displaystyle{E}={0.5}\times{10}^{{6}}$$ psi, that the maximum allowable normal stress is 6ksi, and that the length of the thread must notincrease by more than 1%, determine the required diamter of thethread.
An equation that expresses a relationship between two or more variables, such as $$H = \frac{9}{10} (20 - a)$$ is called a/an ? The process of finding such equations to describe real-world phenomena is called mathematical ? Such equations, together with the meaning assigned to the variables, are called mathematical ?