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vova2212 [387]
3 years ago
6

Sarah has £135

Mathematics
1 answer:
pogonyaev3 years ago
3 0

Answer:

£10 pounds

Step-by-step explanation:

135+70+35 = 240 pounds between all 3

3:2:1 ratio means 6x represents all of them

6x=240

x=£40 each 1

3(40) =  £120 Sarah

2(40) = £80  Gemma

1(40+ = £40  Beth

Gemma received 10 pounds.

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A company manufactures two different sizes of boat lifts. The smaller lift requires 1 hour in the welding department and 2 hours
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Answer:

  • The solution that optimizes the profit is producing 0 small lifts and 50 large lifts.
  • Below are all the steps explained in detail.
  • The graph is attached.

Explanation:

<u />

<u>1. Name the variables:</u>

  • x: number of smaller lifts
  • y: number of larger lifts

<u></u>

<u>2.  Build a table to determine the number of hours each lift requires from each department:</u>

<u></u>

Number of hours

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<u>3. Constraints</u>

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  • 120 hours available in packaging:   2x + y ≤ 120
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Then you must:

  • draw the lines and regions defined by each constraint
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<u></u>

<u>4. Graph</u>

See the graph attached.

Here is how you draw it.

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  • draw the line x + 3y = 150 (a solid line because it is included in the solution set)
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  • draw the line 2x + y ≤ 120 (a solid line because it is included in the solution set)
  • shade the region below and to the left of the line

  • x ≥ 0 and y ≥ 0: means that only the first quadrant is considered

  • the solution region is the intersection of the regions described above.

  • take the points that are vertices inside the solutoin region.

<u>5. Test the profit function for each vertex</u>

The profit function is P(x,y) = 25x + 90y

The vertices shown in the graph are:

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Thus, the solution that optimizes the profit is producing 0 smaller lifts and 90 larger lifts.

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