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makvit [3.9K]
2 years ago
5

a manufacturer has determined that if his company sells x items per day then their profit is given by P=-x^2+ 700 x-10000 euros.

. How many items must be sold each day in order to make a profit
Mathematics
1 answer:
Radda [10]2 years ago
3 0

Answer:

15

Step-by-step explanation:

To find the minimum amount of items, x, that need to be sold for the manufacturer to make a profit, we can use the quadratic formula

x = \frac{-b+\sqrt{b^{2}-4ac } }{2a}; x=  \frac{-b-\sqrt{b^{2}-4ac } }{2a}

x= \frac{-700+\sqrt{700^{2}-4(a)(-10000) } }{2(1)}; x= \frac{-700-\sqrt{700^{2}-4(a)(-10000) } }{2(1)}

x= \frac{-700+\sqrt{530000} }{2}; x= \frac{-700-\sqrt{530000} }{2}

x=\frac{-700+100\sqrt{53} }{2}; x=\frac{-700-100\sqrt{53} }{2};

x=-350 + 50\sqrt53 = 14.005; x = -350 - 50\sqrt53 = -714.005

In context of the problem, we can only rely on the positive value, as the negative value would lead to a loss of profit.

(-714.005)^2+700(-714.005)-10000=-0.360

Furthermore, we must round to the nearest whole number, as you cannot make part of an item.

Lastly, if you were to plug in 14 into the equation for Profit, you would still have a negative number (i.e. a negative profit), thus requiring the manufacturer to make no less than 15 items to make a profit:

(14)^2+700(14)-10000=-4\\\\(15)^2+700(15)-10000=725

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Step-by-step explanation:

You simply write down what you see:

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-------------------------+ now we can add them:

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Finally, it makes sense to double check by filling in these answers in the original equations, just to see if no mistakes were made:

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3 years ago
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Andreyy89

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Step-by-step explanation:

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3 years ago
a building with a height of 32m casts a shadow that is 20m long. a person standing casts a shadow that is 1.2 m long how tall is
wlad13 [49]
Most of the information's required for solving the question is already given in the question.
Height of the building that casts a shadow of 20 m = 32 m
Then
Height of the man that casts a shadow of 1.2 m = (32/20) * 1.2 meter
                                                                             = 3.2 * 1.2 meter
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Answer:

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