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shtirl [24]
3 years ago
12

A furniture company makes large and small chairs. A small chair takes 20 minutes of machine time and 60 minutes of labor to buil

d. A large chair takes 50 minutes
of machine time and 90 minutes of labor to build. The company has 66 hours of labor time and 30 hours of machine time available each day. How many of each
type of chair is built in a day?
Mathematics
1 answer:
bixtya [17]3 years ago
4 0

9514 1404 393

Answer:

  30 small chairs and 24 large chairs

Step-by-step explanation:

Let x and y represent the numbers of small chairs and large chairs built in a day. Then the relations for using available time are ...

  20x +50y = 30×60

  60x +90y = 66×60

Removing common factors, these can be written in standard form as ...

  2x +5y = 180

  2x +3y = 132

Subtracting the second equation from the first gives ...

  2y = 48

  y = 24 . . . . . divide by 2

Using the first equation to find x, we have ...

  2x +5(24) = 180

  2x = 60 . . . . . . . . . . subtract 120

  x = 30 . . . . . . . . divide by 2

The company can build 30 small chairs and 24 large chairs in a day.

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The total monthly profit for a firm is P(x)=6400x−18x^2− (1/3)x^3−40000 dollars, where x is the number of units sold. A maximum
wlad13 [49]

Answer:

Maximum profits are earned when x = 64 that is when 64 units are sold.

Maximum Profit = P(64) = 2,08,490.666667$

Step-by-step explanation:

We are given the following information:P(x) = 6400x - 18x^2 - \frac{x^3}{3} - 40000, where P(x) is the profit function.

We will use double derivative test to find maximum profit.

Differentiating P(x) with respect to x and equating to zero, we get,

\displaystyle\frac{d(P(x))}{dx} = 6400 - 36x - x^2

Equating it to zero we get,

x^2 + 36x - 6400 = 0

We use the quadratic formula to find the values of x:

x = \displaystyle\frac{-b \pm \sqrt{b^2 - 4ac} }{2a}, where a, b and c are coefficients of x^2, x^1 , x^0 respectively.

Putting these value we get x = -100, 64

Now, again differentiating

\displaystyle\frac{d^2(P(x))}{dx^2} = -36 - 2x

At x = 64,  \displaystyle\frac{d^2(P(x))}{dx^2} < 0

Hence, maxima occurs at x = 64.

Therefore, maximum profits are earned when x = 64 that is when 64 units are sold.

Maximum Profit = P(64) = 2,08,490.666667$

6 0
3 years ago
Is 1.7x^2 + 3.5 a cubic polynomial?
devlian [24]

Answer:

No, it is not.

Step-by-step explanation:

This is because if you look at the expression, there is no term that is raised to the cube root. As a result, this isn't a cubic polynomial. However, this would be a quadratic polynomial cause the highest raised exponent is 2, which is the number for quadratic.

If you liked my response, please consider giving me a Brainliest! Thanks!

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