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jeyben [28]
3 years ago
6

Indicate whether each of the following statements is true or false (brie y explain your reason). (a) [1pt] Consider a standard L

P with four variables and three constraints. Then two basic solutions (0; 0; 0; 4; 0; 12; 18) and (3; 0; 0; 1; 0; 2; 0) are adjacent. (b) [1pt] If a linear program has no optimal
Mathematics
1 answer:
prohojiy [21]3 years ago
6 0

Answer:

Indicate whether each of the following statements is true or false (brie y explain your reason). (a) [1pt] Consider a standard LP with four variables and three constraints. Then two basic solutions (0; 0; 0; 4; 0; 12; 18) and (3; 0; 0; 1; 0; 2; 0) are adjacent. (b) [1pt] If a linear program has no optimal solution, then it must have an unbounded feasible region. (c) [1pt] Consider the shadow prices of a standard form of LP. The vector formed by the shadow prices is a feasible solution of the dual problem of this LP. (d) [1pt] A linear program can have exactly 10 feasible solutions. (e) [1pt] Consider a primal problem of maximizing c^Tx and a dual problem of minimizing b^Ty (both subject to some constraints). If for a primal feasible solution x and a dual solution y, we have c^Tx > b^Ty, then y must be dual infeasible. (i.e not a feasible solution for the dual problem). (f) [1pt] In a two player zero sum game, there exists at least one Nash equilibrium.

Step-by-step explanation:

a. true

Because two basic feasible solution stands to be adjacent in case they possess basic variable in common. Two distinct basic solutions with respect to set related with linear constraint under is considered to be adjacent.

b.False.

If a linear problem has no solution it may have null feasible region not important to have unbounded feasible region.

c.True.

If Shadow price is feasible for standard form of LP then it will be feasible solution of dual problem of this LP.

d. False.

As there will be 'n' variables 'm' constraints having nCm feasible solutions.

e.True.

As stated in weak duality theorem

f.True

For every zero-sum 2-player normal-form game, a Nash equilibrium exists. Moreover, a pair of mixed strategies (p,q)(p,q) for the two players is a Nash equilibrium if and only if each strategy is a maximin strategy.

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Will give 30 points!<br> What is a expanded notation?
gavmur [86]

Answer:

It is the number written out to show each digit

Step-by-step explanation:

Let's say you have the number 459

you write out the hundredths place, which is 4 times 100

you write out the tenths place which is 5 times 10

and you write out the oneths place which is 9 times 1

the full thing written out is 459 = 100×4 + 5×10 + 9 × 1

4 0
3 years ago
Akram ed a busniess with rs 70000.After 3months Aslam joined the busniess with rs 40000 and after 6months Asghar also invested r
Crazy boy [7]

Answer:

11858 for akram

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2 years ago
A class has $90 to spend on a field trip. The field trip costs $2.50 per person and there will be 5 chaperones on the trip. One
vodka [1.7K]

Answer:

Step-by-step explanation:

x is the number of students

(x+5) is the number of students and chaperons

$2.50·(x+5) is the amount of money the number of students and chaperons will pay for the trip, and that number should be less or equal than $90 because those are all the money they have

2.50(x+5) ≤ 90 which is the same as 90 ≥ 2.50(x+5)

The inequality "90 greater-than 2.50 (x + 5) "

90 > 2.50(x+5) is an error becase it excludes the possibility that <u>the trip can cost exact $90</u> so we need not just greater than > , yet greater and equal than ≥ sign

90 ≥ 2.50(x+5)

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2 years ago
QUESTION IS DOW BELOW 5 POINTS EACH PLEASE HELP PLEASE HELP PLEASE HELP
masha68 [24]

The central angle in the circle is ∠DAC,major arc is BED, minor arc is ADC and BC=(5π*BD)/18.

Given that BD is diameter of the circle and angle BAC is 100°.

We are required to find the central angle, major arc, minor arc, m BEC, BC.

Angle is basically finding out the intensity of inclination of something on the surface.

In the circle central angles are many like BAC and CAD. We can write CAD as DAC also.

Major arc of a circle is that arc whose length is larger than all other arcs in the circle.

In our circle the major arc is arc BED.

Minor arc of a circle is that arc whose length is smaller.

In our circle the minor arc is arc ADC.

We know that arc's length is 2πr(Θ/360)

In this way BC=2π*(BD/2)*100/360

=(5π*BD)/18

We cannot find angle BEC.

Hence the central angle in the circle is ∠DAC,major arc is BED, minor arc is ADC and BC=(5π*BA)/18.

Learn more about angles at brainly.com/question/25716982

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2 years ago
Please help me somebody!!! I really struggle with this in math class!
Tresset [83]

Answer:

y - 9 = -\frac{4}{3}(x - 3)  

Step-by-step explanation:

Given the points (3, 9) and (9, 1), we must first solve for the slope of the line before proceeding with writing the point-slope form.

In order to solve for the slope (<em>m </em>), use the following formula:

m = (y₂ - y₁)/(x₂ - x₁)

Let (x₁, y₁) =  (3, 9)

     (x₂, y₂) = (9, 1)

Substitute these values into the given formula:

m = (y₂ - y₁)/(x₂ - x₁)

m = (1 - 9)/(9 - 3)

m = \frac{-8}{6} = \frac{-4}{3}

Therefore, the slope of the line, m = -4/3.

Next, using the slope, m = -4/3, and one of the given points, (x₁, y₁) = (3, 9), substitute these values into the following point-slope form:

y - y₁ = m(x - x₁)

y - 9 = -\frac{4}{3}(x - 3)  ⇒ This is the <u>point-slope form</u>.

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