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Svet_ta [14]
3 years ago
10

A manufacturer makes two types of handmade fancy paper bags. Type A and Type B. Two designers a cutter and a finisher need to wo

rk on both kinds of bags. A type A bag requires 2 hours of the cutters time and 3 hours of the finishers time. A type B bag requires 3 hours of the cutters time and 1 hour of the finishers time. Each month the cutter is available for 108 hours and the finisher is available 78 hours. The manufacturer gets a profit of $12 for each bag of type A and $9 for each bag of type B. Identify the number of bags for each type to be manufactured to obtain the maximum profit.

Mathematics
1 answer:
Vlad1618 [11]3 years ago
4 0

Answer:

  • 18 Type A bags
  • 24 Type B bags

Step-by-step explanation:

The graph shows the constraints and the boundaries of the feasible region. The maximum profit will be had with the manufacture of 18 Type A bags and 24 Type B bags.

__

The inequality describing the constraint on cutter hours is ...

  2a +3b ≤ 108

The inequality describing the constraint on finisher hours is ...

  3a +1b ≤ 78

The boundary lines of the solution regions of these inequalities intersect at ...

  (a, b) = (18, 24)

The profit function is such that it doesn't pay to make all of one type or the other bags. The most profit is had for the mix ...

  18 Type A bags; 24 Type B bags.

On the graph, the line representing the profit function will be as far as possible from the origin at the point of maximum profit.

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Gwar [14]

Answer:

Step-by-step explanation:

First count the number of sides. There are 6 sides.

Now use the formula

(n - 2) * 180  To determine the total of all 6 angles.

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4 * 180 = 720

Is that a 9 in x + 9 [lower left]? I'll assume so. Edited to show it was a 4.

x + 4 + 120 + x + 50 + 140 + 112 + x = 720     Combine

3x + 4 + 120 + 50 + 140 + 112 = 720

3x + 426 = 720                                                Subtract 431 from both sides

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Nata [24]

Answers:

Gabe needs 30 liters of the 50% solution

Gabe needs 30 liters of the 70% solution

Both answers are 30

==================================

Explanation:

We have two beakers, each of which we don't know how much is inside. Let's call this x and y

x = amount of liquid in the first beaker (water+acid)

y = amount of liquid in the second beaker (water+acid)

We're told that the beakers have a 50% solution and a 70% solution of acid. This means that the first beaker has 0.5*x liters of pure acid, and the second beaker has 0.7*y liters of pure acid. In total, there is 0.5x+0.7y liters of pure acid when we combine the two beakers. This is out of x+y = 60 liters total, which we can solve for y to get y = 60-x. We will use y = 60-x later on when it comes to the substitution step

We can divide the total amount of pure acid (0.5x+0.7y liters) over the total amount of solution (x+y = 60) to get the following

(0.5x+0.7y)/(x+y) = (0.5x+0.7y)/60

We want this to be equal to 0.6 because Gabe wants a 60% solution when everything is said and done, so

(0.5x+0.7y)/60 = 0.60

0.5x+0.7y = 0.60*60 .... multiply both sides by 60

0.5x+0.7y = 36

0.5x+0.7( y ) = 36

0.5x+0.7(60-x) = 36 ........ replace y with 60-x (substitution step)

0.5x+0.7(60)+0.7(-x) = 36 .... distribute

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-0.2x = 36-42 .... subtract 42 from both sides

-0.2x = -6

x = -6/(-0.2) .... divide both sides by -0.2

x = 30

He needs 30 liters of the 50% solution

Use this x value to find y

y = 60-x

y = 60-30

y = 30

So he needs 30 liters of the 70% solution


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Vesna [10]

Answer:

your answer is 13.

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Solve <br><br> 9x-14-2x=5(2x-6)
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