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laiz [17]
3 years ago
6

98 POINTS LINEAR PROGRAMMING

Mathematics
1 answer:
valina [46]3 years ago
6 0

P = printer

M = microwave

Weight Equation: 20P + 30M = 1600

Size equation: 3P + 2M = 150


Solve Weight Equation:

20P + 30M = 1600

Subtract 30M from each side:

20P = 1600 - 30M

Divide both sides by 20:

P = 80 - 3/2M


Replace P in size equation with above:

3(80 - 3/2M) + 2M = 150

240 - 4.5M + 2M = 150

240-2.5M = 150

Subtract 240 from each side:

-2.5M = -90

Divide both sides by -2.5:

M = 36


Now solve for P:

3P + 2(36) = 150

3P = 72 = 150

3P = 78

P = 78/3

P = 26


26 Printers and 36 Microwaves.


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1)

n         1          2         3           4         5         6

f(n)    1033    932     831      730     629     528

First term (a₁):  <u>1033 </u>          Common difference (d): <u>-101 </u>

Explicit rule:  a_{n} = 1134 - 101n    Recursive rule: a_{n} = a_{n-1} - 101

a_{n} = a_{1} + d(n - 1)

a_{n} = 1033 - 101(n - 1)

a_{n} = 1033 - 101n + 101

a_{n} = 1134 - 101n

***********************************************************************************

2)

n         1          2         3           4         5         6

f(n)   -39      -29       -19        -9          9        19

First term (a₁):  <u> -39  </u>          Common difference (d): <u> +10  </u>

Explicit rule:  a_{n} = -49 + 10n    Recursive rule: a_{n} = a_{n-1} + 10

a_{n} = a_{1} + d(n - 1)

a_{n} = -39 + 10(n - 1)

a_{n} = -39 + 10n - 10

a_{n} = -49 + 10n

***********************************************************************************

3)

n         1          2         3           4         5         6

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a_{n} = a_{1} + d(n - 1)

a_{n} = 3.75 - 1.25(n - 1)

a_{n} = 3.75 - 1.25n + 1.25

a_{n} = 5 - 1.25n


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