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Andreyy89
3 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?
Mathematics
1 answer:
densk [106]3 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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6 0
3 years ago
A class of 340 students went on a field trip.
ipn [44]

Answer: 2 cars and 6 buses.

Step-by-step explanation:

x + y = 8

5x + 55y =

5 times 2 = 10

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55 times 6 = 330

Add 330 plus 10 = 340!

5 0
3 years ago
Find the function of which is the solution of 36y"-48y'-48y=0 with initial conditions y1(0)=1. y1'(0)=0
lilavasa [31]

Answer:

y=\frac{1}{4} e^{2x}+\frac{3}{4} e^{-\frac{2}{3}x }

Step-by-step explanation:

Let,  D=\frac{d}{dx}

Now, us simplify the given differential equation and write it in terms of D,

36y''-48y'-48y=0

or, 3y''-4y'-4y=0

or, (3D^2-4D-4)y=0

We have our auxiliary equation:

3D^2-4D-4=0

or, (3D+2)(D-2)=0

or, D=2, - \frac{2}{3}

Therefore our solution is,

y=Ae^{2x}+Be^{- \frac{2}{3}x}

and, y'=2Ae^{2x}-\frac{2}{3}Be^{\frac{2}{3}x }

Applying the boundary conditions, we get,

A+B=1

2A-\frac{2}{3}B=0

Solving them gives us,

A=\frac{1}{4} ,B=\frac{3}{4}

Hence,

y=\frac{1}{4} e^{2x}+\frac{3}{4} e^{-\frac{2}{3}x }

4 0
3 years ago
What is franks commission if he sales $12,500 of an item and his commission rate is 8.5%
Licemer1 [7]
<h3>SOLUTION:</h3>

Given,

Total sale = $12,500

Rate = 8.5%

Therefore, Commission

= 12,500 × 8.5%

= 12,500 × 85/1000

= 1062.5

5 0
3 years ago
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Paul [167]

Answer:

The claim made by the researcher lacks the validity on basis of reasons as indicated in the explanation.

Step-by-step explanation:

The claim made by the researcher is not valid on basis of following reasons:

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3 years ago
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