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Crazy boy [7]
3 years ago
11

Please Help ASAP! Will name Brainliest! Question: Minimize the objective function P = 5x + 8y for the given constraints. x ≥ 0 y

≥ 0 2x + 3y ≥ 15 3x + 2y ≥ 15 Answer: 25, 46, 39, 37.5

Mathematics
1 answer:
maksim [4K]3 years ago
3 0

Answer:

Option D.

Step-by-step explanation:

Minimize the objective function P = 5x + 8y for the given constraints.

x\geq 0,y\geq 0

2x+3y\geq 15

3x+2y\geq 15

The related equations of above inequalities are

2x+3y=15

3x+2y=15

For 2x+3y=15,

x     y

0     5

7.5   0  

Plot (0,5) and (7.5,0) and join them by straight line.

For 3x+2y=15,

x     y

0     7.5

5      0  

Plot (0,7.5) and (5,0) and join them by straight line.

Check the inequalities for (0,0).

2(0)+3(0)\geq 15\Rightarrow 0\geq 15 False

3(0)+2(0)\geq 15\Rightarrow 0\geq 15 False

It means both lines are solid lines and shaded region for each lies opposite side of (0,0).

From the below graph it is clear that the vertices of feasible region are (0,7.5), (3,3), (7.5,0).

Point       P = 5x + 8y

(0,7.5)     P=5(0)+8(7.5)=60

(3,3)     P=5(3)+8(3)=15+24=39

(7.5,0)     P=5(7.5)+8(0)=37.5 (Minimum)

So, minimum value is 37.5.

Therefore, the correct option is D.

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3x + 2 ≤ 14 <br><br>-5 + 2x &gt; 15 * <br><br>-2x + 4 ≥ 18 <br><br>HaLp i don't gets
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9514 1404 393

Answer:

  1. x ≤ 4
  2. x > 10
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Step-by-step explanation:

We're guessing you want to solve for x in each case. You do this in basically the same way you would solve an equation.

1. 3x +2 ≤ 14

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2. -5 +2x > 15

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3. -2x +4 ≥ 18

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_____

<em>Additional comment</em>

The statement above that the same methods for solving apply to both equations and inequalities has an exception. The exception is that some operations reverse the order of numbers, so make the inequality symbol reverse. The usual operations we're concerned with are <em>multiplication and division by a negative number</em>: -2 < -1; 2 > 1, for example. There are other such operations, but they tend to be used more rarely for inequalities.

You will note that we avoided division by -2 in the solution of the third inequality by adding 2x to both sides, effectively giving the variable term a positive coefficient. You will notice that also changes its relation to the inequality symbol, just as if we had left the term where it was and reversed the symbol: -2x ≥ 14 ⇔ -14 ≥ 2x ⇔ x ≤ -7 ⇔ -7 ≥ x

5 0
3 years ago
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jenny wrapped 30 gifts,jenny wrapped 5 times as many gifts as hong let n be the number of gifts that hong wrapped
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7 0
3 years ago
Read 2 more answers
Which is the answer to this?
Vinil7 [7]
TanB=CA/AB
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=option D.


HOPE IT HELPS YOU '_'
8 0
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