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Kisachek [45]
3 years ago
8

. A one-product firm estimates that its daily total cost function (in suitable units) is C (x) = x^3 - 6x^2 + 13x + 15 and its t

otal revenue function is R(x) = 28x. Find the value of x that maximizes the daily profit. (4 points)
Business
1 answer:
givi [52]3 years ago
8 0

Answer:

Value of x maximising profit : x = 5

Explanation:

Cost : C(x) = x^3 - 6x^2 + 13x + 15 ; Revenue: R(x) = 28x

Profit : Revenue - Cost = R(x) - C(x)

28x - [x^3 - 6x^2 + 13x + 15]  = 28x - x^3 + 6x^2 - 13x - 15

= - x^3 +  6x^2 + 15x - 15

To find value of 'x' that maximises total profit , we differentiate total profit function with respect to x & find that x value.

dTP/dx = - 3x^2 + 12x + 15 = 0 ► 3x^2 - 12x - 15 = 0

3x^2 + 3x - 15x - 15 = 0  ► 3x (x +1) - 15 (x + 1) = 0 ► (x+1) (3x-15) = 0

x + 1 = 0 ∴ x = -1   [Rejected, production quantity cant be negative] ;

3x - 15 = 0 ∴ 3x = 15 ∴ x = 15/3 = 5

Double derivate : d^2TP/dx^2 = - 6x + 12

d^2TP/dx^2  i.e - 6x + 12  at x = 5 is -6(5) + 12 = - 30+ 12 = -8 which is negative. So profit function is maximum at x = 5

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Explanation:

The equal marginal principle refers to the principle in which the consumer would select that combination of goods which maximise its total utility. It could be selected by having marginal utility and its price

And for profit maximization, the marginal utility and the price is equivalent to both the goods.

i.e

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<h3>What is the Correlation Method?</h3>

The correlation method is the method utilized in the sales comparison approach where more importance is given to two properties being compared against some others.

The sales comparison approach itself is used in analyzing the worth of a property by comparing it to others that have been sold in recent times.

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