5(2x-8) in distributive property

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

I will give brainliest to best answer

lorasvet [3.4K]

That's a Congruent Triangle question.

The first thing that we should to analize is it: What figure is EFGH? The question say for us that $\overline{EF} \cong \overline{GH}$ and $\overline{EH} \cong \overline{GF}$ , therefore, EFGH is a parallelogram because its parallel sides are congruents (equals).

Now, we should to proof that $\triangle EFH \cong \triangle GHF$ . The simbol "≅" means congruence, that is, $\triangle EFH \cong \triangle GHF$ means that the triangles EFH and GHF are equals.

Let's proof:

$\overline{HF}$ is a diagonal of the parallelogram EFGH. When we have a diagonal in a parallelogram, the opposite angles are congruents (look at the picture: the blue angles are congruent and the red angles are congruents too). Therefore, $E\hat{F}H \cong F\hat{H}G$ and $E\hat{H}F \cong H\hat{F}G$ .

Both triangle has a comum side: the diagonal $\overline{HF}$ . The diagonal $\overline{HF}$ is between two angles that we know that are congruents, Therefore, by the case ASA (Angle, Side, Angle), we proof that $\triangle EFH \cong \triangle GHF$ .