Could you help me to solve the problem below the cost for producing x items is 50x+300 and the revenue for selling x items is 90x−0.5^2 the company makes is how much it takes in (revenue) minus how much it spends (cost). Recall that profit is revenue minus cost. Set up an expression for the profit from producing and selling x items. Find two values of x that will create a profit of $300. Is it possible for the company to make a profit of $15,000?

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CainTheManmeat CainTheManmeat · Answer 1 · 2020-09-17T21:12:38+02:00

Answer:

Profit function: P(x) = -0.5x^2 + 40x - 300

profit of $50: x = 10 and x = 70

NOT possible to make a profit of $2,500, because maximum profit is $500

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shivishivangi1679 shivishivangi1679 · Answer 2 · 2022-07-25T13:50:33+02:00

The maximum profit is of $500, So it is impossible to achieve the profit of $2500.

Profit = Revenue - Cost

Given information:

The function which shows revenue is [tex]90x-0.5x^2[/tex]

The cost function [tex]C(x) = 50x+300[/tex]

[tex]R(x) = 90x-0.5x^2[/tex]

Profit = Revenue - Cost

[tex]P(x) = 90x-0.5x^2 - 50x - 300\\\\P(x) =-0.5x^2 - 40x - 300[/tex]

On equating with profit of $50,

We get,

[tex]P(x) =-0.5x^2 - 40x - 300\\\\50 =-0.5x^2 - 40x - 300\\\\x^{2} - 80x +700 = 0[/tex]

The profit of $50: x = 10 and x = 70

Hence, for the maximum value of profit the coordinate of vertex is given;

x = 80 / 2 = 40

Putting the above value in profit equation

[tex]x^{2} - 80x +700 = 0\\\\40^{2} - 80(40) +700 \\\\P(40) = 500[/tex]

Hence, the maximum profit is of $500, So it is impossible to achieve the profit of $2500.

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