A company is selling product x, which has demand ntion of p=52-2x and the total cost function of TC=3x^2+2x+10. the marginal revenue and marginal cost functions are;
a) MR=52-2X and MC=6x+2
b) MR=52-4x and MC=6x+2
c) MR=52-2X and MC=6x
d) MR=52-4x and MC=6x+2
To determine the correct option for the marginal revenue (MR) and marginal cost (MC) functions, we need to understand the definitions of MR and MC and how they are derived from the demand and cost functions.
Marginal revenue (MR) is the additional revenue a company earns by selling one more unit of a product. In this case, MR can be calculated by taking the derivative of the demand function with respect to quantity (x).
Similarly, marginal cost (MC) is the additional cost a company incurs by producing one more unit of a product. In this case, MC can be calculated by taking the derivative of the total cost function with respect to quantity (x).
Given the demand function p=52-2x, we can find MR by differentiating the equation with respect to x:
dp/dx = d(52-2x)/dx
= -2
Therefore, the marginal revenue function is MR = -2.
Given the total cost function TC=3x^2+2x+10, we can find MC by differentiating the equation with respect to x:
dTC/dx = d(3x^2+2x+10)/dx
= 6x + 2
Therefore, the marginal cost function is MC = 6x + 2.
Comparing the calculated MR and MC functions with the given options, we can see that the correct option is:
a) MR = 52-2x and MC = 6x + 2