Find the midpoint of the line segment with the given endpoints (9, -8) (-10, -2)

State the linear programming problem in mathematical terms, identifying the objective function and the constraints. A firm makes

Sedbober [7]

Answer:

Maximum profit at (3,0) is $27.

Step-by-step explanation:

Let quantity of products A=x

Quantity of products B=y

Product A takes time on machine L=2 hours

Product A takes time on machine M=2 hours

Product B takes time on machineL= 4 hours

Product B takes time on machine M=3 hours

Machine L can used total time= 8hours

Machine M can used total time= 6hours

Profit on product A= $9

Profit on product B=$7

According to question

Objective function Z= $9x+7y$

Constraints:

$2x+3y\leq 6$

$2x+4y\leq 8$

Where $x\geq 0, y\geq 0$

I equation $2x+3y\leq 6$

I equation in inequality change into equality we get

$2x+3y=6$

Put x=0 then we get

y=2

If we put y=0 then we get

x= 3

Therefore , we get two points A (0,2) and B (3,0) and plot the graph for equation I

Now put x=0 and y=0 in I equation in inequality

Then we get $0\leq 6$

Hence, this equation is true then shaded regoin is below the line .

Similarly , for II equation

First change inequality equation into equality equation

we get $2x+4y=8$

Put x= 0 then we get

y=2

Put y=0 Then we get

x=4

Therefore, we get two points C(0,2)a nd D(4,0) and plot the graph for equation II

Point A and C are same

Put x=0 and y=0 in the in inequality equation II then we get

$0\leq 8$

Hence, this equation is true .Therefore, the shaded region is below the line.

By graph we can see both line intersect at the points A(0,2)

The feasible region is AOBA and bounded.

To find the value of objective function on points

A (0,2), O(0,0) and B(3,0)

Put A(0,2)

Z= $9\times 0+7\times 2=14$

At point O(0,0)

Z=0

At point B(3,0)

Z= $9\times3+7\times0=27$

Hence maximum value of z= 27 at point B(3,0)

Therefore, the maximum profit is $27.

6 0

4 years ago

What is 75% of 140? 65 75 95 105

monitta

Answer:

105

Step-by-step explanation:

75 percent *140 =

(75:100)*140 =

(75*140):100 =

10500:100 = 105

Now we have: 75 percent of 140 = 105

Question: What is 75 percent of 140?

Percentage solution with steps:

Step 1: Our output value is 140.

Step 2: We represent the unknown value with $x$.

Step 3: From step 1 above,$140=100\%$.

Step 4: Similarly, $x=75\%$.

Step 5: This results in a pair of simple equations:

$140=100\%(1)$.

$x=75\%(2)$.

Step 6: By dividing equation 1 by equation 2 and noting that both the RHS (right hand side) of both

equations have the same unit (%); we have

$\frac{140}{x}=\frac{100\%}{75\%}$

Step 7: Again, the reciprocal of both sides gives

$\frac{x}{140}=\frac{75}{100}$

$\Rightarrow x=105$

Therefore, 75\% of 140is 105

8 0

3 years ago

Read 2 more answers

Suppose that only 65% of all drivers in a certain state wear a seat belt. a random sample of 80 drivers is selected. what is the

jonny [76]

Answer:

Pr(X >42) = Pr( Z > -2.344)

= Pr( Z< 2.344) = 0.9905

Step-by-step explanation:

The scenario presented can be modeled by a binomial model;

The probability of success is, p = 0.65

There are n = 80 independent trials

Let X denote the number of drivers that wear a seat belt, then we are to find the probability that X is greater than 42;

Pr(X > 42)

In this case we can use the normal approximation to the binomial model;

mu = n*p = 80(0.65) = 52

sigma^2 = n*p*(1-p) = 18.2

Pr(X >42) = Pr( Z > -2.344)

= Pr( Z< 2.344) = 0.9905

7 0

3 years ago

Match each graph with the correct cosine function based on its period.

earnstyle [38]

Answer:

1. cos (x/2)

2.y=cos(4x)

3. y=cos(x)

4.y= cos(x/4)

Step-by-step explanation:

The graph of cosine function is sinusoidal and the y value ranges between -1 to 1.

the cosine function is periodic with general period P of 2π

if P< 2π then cosine graph experience a compression horizontally

if P>2π then cosine graph experience a stretch horizontally

for graph 1, the period is 4π hence the graph is stretched with period of 4π

for graph 2, the period is π/2 hence the graph is compressed with period of π/2

for graph 3, the period is 2π hence the graph is periodic with period of 2π

for graph 4, the period is 8π hence the graph is stretched with period of 4π

!

3 0

3 years ago

Give three solutions of the inequality 6-11x<61

Alex17521 [72]

I hope this helps you

6-61 <11x

-55 <11x

-5 <x

3 0

4 years ago

Read 2 more answers