Answer:
tc = (5^3)/3 - (5^2) + 11(5)
Explanation:
The total cost function is given as: tc = x^3/3 - x^2 + 11x.
The total cost function represents the total cost incurred in producing a certain quantity of a good or providing a service. In this case, the total cost is a function of the quantity produced or provided, represented by the variable x.
Let's break down the components of the total cost function:
1. The term x^3/3 represents the cost associated with the production of x units. The exponent of 3 indicates that the cost increases rapidly as the quantity produced increases.
2. The term -x^2 represents a cost component that decreases as the quantity produced increases. The exponent of 2 indicates that the cost decreases at a decreasing rate.
3. The term 11x represents a cost component that increases linearly with the quantity produced. This term could represent fixed costs or costs that are directly proportional to the quantity produced.
By combining these three terms, we obtain the total cost function tc.
To find specific cost values, you can substitute different values for x into the total cost function. For example, if you want to find the total cost when x equals 5, you can substitute x = 5 into the function:
tc = (5^3)/3 - (5^2) + 11(5)
Simplifying the equation will give you the total cost associated with producing or providing 5 units.
It is important to note that the total cost function can vary depending on the specific context or assumptions of the problem. However, in this case, the given total cost function represents the relationship between quantity produced (x) and the corresponding total cost (tc).