contestada

Find the maximum profit and the number of units that must be produced and sold in order to yield the maximum profit. Assume that​ revenue, Upper R left parenthesis x right parenthesisR(x)​, and​ cost, Upper C left parenthesis x right parenthesisC(x)​, of producing x units are in dollars. Upper R left parenthesis x right parenthesisR(x)equals=4 x4x​, Upper C left parenthesis x right parenthesisC(x)equals=0.01 x squared plus 0.3 x plus 40.01x2+0.3x+4

Respuesta :

Answer:

185 units

Step-by-step explanation:

Given,

The revenue function is,

[tex]R(x) = 4x[/tex]

Cost function,

[tex]C(x) = 0.01x^2 + 0.3x + 4[/tex],

Where,

x = number of units produced.

Thus, profit = revenue - cost

[tex]P(x) = 4x - ( 0.01x^2 + 0.3x + 4) = -0.01x^2 + 3.7x - 4[/tex]

Differentiating with respect to x,

[tex]P'(x) = -0.02x + 3.7[/tex]

Again differentiating with respect to x,

[tex]P''(x) = -0.02[/tex]

For maxima or minima,

P'(x) = 0,

[tex]-0.02x + 3.7x =0[/tex]

[tex]-0.02x = -3.7[/tex]

[tex]\implies x = \frac{3.7}{0.02}=185[/tex]

For x = 185,

P''(x) = negative,

Hence, for maximising the profit 185 units must be produced.

Otras preguntas