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A company manufactures and sells x cellphones per week. The weekly​ price-demand and cost equations are given below. p equals 600 minus 0.5 x and Upper C (x )equals 15 comma 000 plus 130 x ​(A) What price should the company charge for the​ phones, and how many phones should be produced to maximize the weekly​ revenue

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pedrocarratore

Answer:

Price = 300

x = 600 units

Step-by-step explanation:

Let 'x' be the number of units sold

Price is given by:

[tex]P(x) = 600 - 0.5x[/tex]

Cost of production is given by:

[tex]C(x) =15,000+130x[/tex]

Revenue is defined as:

[tex]R(x) = xP(x)\\R(x) = x(600-0.5x) = 600x - 0.5x^2[/tex]

The value of 'x' for which the derivate of the revenue function is zero, yields the number of phones sold that maximizes profit:

[tex]\frac{dR(x)}{dx} = 600 - x = 0\\ x= 600[/tex]

The price at this output level is:

[tex]P(x) = 600 - 0.5x\\P(x) = 600 - 0.5*600\\P(x) = 300[/tex]

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