Find the minimum value of C = 4x + 3y
Subject to the following constraints:
x > 0
y > 0
2x + 3y > 6
3x – 2y < 9
x + 5y = 20

2x + 3y > 6                                                                                                          (1)

3x – 2y = 9                                                                                                         (2)

x + 5y = 20                                                                                                        (3)

From (1) and (2), we have:

(2x + 3y) - (3x - 2y) > 6 - 9

5y - x > -3                                                                                                          (4)

From (3) and (4), we have:

(x + 5y) - (5y - x) > 20 - (-3)

2x > 23

x > 12,5                                                                                                               (5)

From (3) and (5), we have:

x + 5y = 20 ⇔ 12,5 + 5y > 20

5y > 7,5

y > 1,5

So: C = 4x + 3y > 12,5 × 4 + 1,5 × 3 = 50 + 4,5 = 54,5

Conclusion: C > 54,5

the figures below are made out of circles, semicircles, quarter … find the area and the perimeter of each figure and give your answers as a completely simplified exact value in terms of π (no approximations). remember that we'll also have to cut whatever areas we get in half, since we're only dealing

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i dont know sorry

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