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mel-nik [20]
3 years ago
5

Find the minimum cost of producing 50,000 units of a product, where x is the number of units of labor (at $36 per unit) and y is

the number of units of capital (at $48 per unit).
(Round your answer to two decimal places.)


P(x, y) = 100x^0.6y^0.4
Mathematics
1 answer:
erastovalidia [21]3 years ago
6 0

Answer:

Step-by-step explanation:

Given problem: C(x,y) = 36x + 48y

constraint: 100x^0.6y^0.4

Using langrange Multiplier,

36 = 0.6(100)x^-0.4y^0.4λ         i

48 = 0.4(100)x^0.6y^-0.6λ         ii

dividing the equations we have:

x = 2y

substituting into the constraint

p(x,y) = 100 *(2y)^0.6 y^0.4 = 100*2^0.6 *y

5000  = 151.572y

y = 329.876 labor units

x = 659.752 capital units

Minimum cost = 36(659.752) +48(329.876) = $39585.12

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The geometric sequence a i a i ​ a, start subscript, i, end subscript is defined by the formula: a 1 = 8 a 1 ​ =8a, start subscr
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Question:

The geometric sequence ai is defined by the formula: a₁ = 8, aᵢ = aᵢ₋₁(-1.5 ).

Find the sum of the first 20 terms in the sequence. Choose 1 answer:

Answer:

The sun of 20 terms of the progress is -10,637.621536256

Step-by-step explanation:

Given

Geometric Sequence

a₁ = 8

aᵢ = aᵢ₋₁(-1.5 )

First, the common ratio needs to be calculated.

The common ratio is the ratio of a term to its previous term.

In other words,

Ratio = 2nd term ÷ 1st term or 3rd term ÷ 2nd term, ...... Etc.

We can calculate the common ratio from aᵢ = aᵢ₋₁(-1.5 ) by dividing both sides by aᵢ₋₁. This gives

aᵢ / aᵢ₋₁ = aᵢ₋₁(-1.5 ) / aᵢ₋₁

aᵢ / aᵢ₋₁ = -1.5

So, the common ratio, r = -1.5

Now that we've had the common ratio and first term to be -1.5 and 8 respectively, the sum of 20 terms can then be calculated using the sum of n terms formula.

Sₙ = a(1 - rⁿ)/(1 - r)

We're making use of this formula because r is less than 1

Where n = 20

a = first term = 8

r = -1.5

By substituting these values; we get

S₂₀ = 8(1 - (-1.5)²⁰)/(1 - (-1.5))

S₂₀ = 8(1 - (-1.5)²⁰)/(1 + 1.5))

S₂₀ = 8(1 - (-1.5)²⁰)/(1 + 1.5))

S₂₀ = 8(1 - (3325.25673008

))/(2.5)

S₂₀ = 8(1 - 3325.25673008

)/(2.5)

S₂₀ = 8(-3324.25673008

)/(2.5)

S₂₀ = -10,637.621536256

5 0
3 years ago
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