4. (10 points) in the study of economics a function that gives the cost c(x) for producing x units of a…

4. (10 points) in the study of economics a function that gives the cost c(x) for producing x units of a commodity is called a cost function. we define the marginal cost as the additional cost to produce one more unit. when the cost function is linear, the marginal cost is the slope of the corresponding line. suppose that c(x) in dollars of producing x bicycles is given by the linear function c(x)=625 + 45x. (a) (4 points) find the cost of producing 10 bicycles. (b) (2 points) what is the marginal cost? (c) (4 points) use the answers in parts (a) and (b) to find the cost of producing 11 bicycles. then check the answer by evaluating c(11).

4. (10 points) in the study of economics a function that gives the cost c(x) for producing x units of a commodity is called a cost function. we define the marginal cost as the additional cost to produce one more unit. when the cost function is linear, the marginal cost is the slope of the corresponding line. suppose that c(x) in dollars of producing x bicycles is given by the linear function c(x)=625 + 45x. (a) (4 points) find the cost of producing 10 bicycles. (b) (2 points) what is the marginal cost? (c) (4 points) use the answers in parts (a) and (b) to find the cost of producing 11 bicycles. then check the answer by evaluating c(11).

Answer

Explanation:

Step1: Substitute x = 10 into cost - function

Given $C(x)=625 + 45x$, when $x = 10$, we have $C(10)=625+45\times10$. $C(10)=625 + 450=1075$.

Step2: Identify the marginal - cost

For a linear cost function $C(x)=mx + b$ (where $m$ is the slope and $b$ is the y - intercept), the marginal cost is the slope of the line. Given $C(x)=625 + 45x$, the marginal cost $MC = 45$.

Step3: Calculate the cost of producing 11 bicycles

We know that the cost of producing 11 bicycles can be found using the cost of producing 10 bicycles and the marginal cost. The cost of producing 11 bicycles $C(11)$ is approximately $C(10)+MC$. Since $C(10) = 1075$ and $MC = 45$, then $C(11)\approx1075 + 45=1120$. We can also directly calculate $C(11)$ by substituting $x = 11$ into the cost function $C(x)=625+45x$. So $C(11)=625+45\times11=625 + 495=1120$.

Answer:

(a) The cost of producing 10 bicycles is $1075$. (b) The marginal cost is $45$. (c) The cost of producing 11 bicycles is $1120$.