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2 years ago

10

The cost, in dollars, of manufacturing x microwaves is 6,000 + 300x dollars. The amount received when selling these x microwaves

is 700x dollars. What is the least number of microwaves that must be manufactured and sold so that the net profit is $2400?

1 answer:

densk [106]2 years ago

4 0

Answer:

21 microwaves

Step-by-step explanation:

The net profile is equal to the income less the total cost, so the equation to the net profile NP is:

NP = 700x - (6000 + 300x)

Where 700x is the income and (6000+300x) is the cost of manufacturing.

Now, replacing NP by 2400 and solving for x, we get:

2400 = 700x - (6000 + 300x)

2400 = 700x - 6000 - 300x

2400 + 6000 = 400x

8400 = 400x

$\frac{8400}{400}=x\\ 21=x$

So, the least number of microwaves that must be manufactured and sold so that the net profit is $2400 is equal to 21.

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<u>Process to balance the scale:</u>

Given that the if one x block is subtracted from the right side and three numbered blocks are subtracted from the left side.

Thus, the equation (1) becomes

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Now, to balance the scale, let us subtract one block x from the left side and subtract three numbered blocks from the right side.

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Step-by-step explanation:

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Answer:

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Step-by-step explanation:

Given that :

Clients are interviewed in groups of 2 on the first day; meaning two persons at a time

Second day, clients are interviewed in groups of 4; meaning 4 persons at a time.

Therefore, if the same number of clients are to be interviewed on each day, the smallest number of clients that could be interviewed each day could be obtained by getting the Least Common Multiple of both numbers: 2 and 4

- - - - 2 - - - 4

2 - - - 1 - - - 2

2 - - - 1 - - - 1

Therefore, the Least common multiple is (2 * 2) = 4

Therefore, the smallest number of clients that could be interviewed each day is 4.

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World poultry production was 77.2 million tons in the year 2004 and increasing at a continuous rate of 1.6% per year. Assume tha

dezoksy [38]

Answer:

A) $P(t)=77.2\cdot e^{0.016t}$

B) 89.157 million tons.

C) In year 2017.

Step-by-step explanation:

We have been given that world poultry production was 77.2 million tons in the year 2004 and increasing at a continuous rate of 1.6% per year.

A). We know that a continuous growth function is in form $y=a\cdot e^{kx}$ , where,

a = Initial value,

k = Growth rate in decimal form.

$1.6\%=\frac{1.6}{100}=0.016$

Upon substituting our given values, we will get:

$P(t)=77.2\cdot e^{0.016t}$

Therefore, our required function would be $P(t)=77.2\cdot e^{0.016t}$ , where, P represents world poultry production, in million tons, as a function of the number of years, t, since 2004.

B) To find the world poultry production in the year 2013, we will substitute $t=2013-2004=9$ in above formula as:

$P(9)=77.2\cdot e^{0.016(9)}$

$P(9)=77.2\cdot e^{0.144}$

$P(9)=77.2\cdot 1.1548841085249135$

$P(9)=89.1570531781\approx 89.157$

Therefore, the world poultry production in the year 2013 would be 89.157 million tons.

C) To find the number of years it will take for world poultry production to be over 95 million tons, we will equate our function with 95 as:

$95=77.2\cdot e^{0.016t}$

Divide both sides by 77.2:

$1.2305699481865285=e^{0.016t}$

Take natural log of both sides:

$\text{ln}(1.2305699481865285)=\text{ln}(e^{0.016t})$

$\text{ln}(1.2305699481865285)=0.016t\text{ln}(e)$

$0.20747743456981035=0.016t*1$

Divide both sides by 0.016:

$t=12.9673396606$

$t\approx 13$

Therefore, 13 years after in 2017 world poultry production goes over 95 million tons.

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