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The concept of marginal cost is commonly used in economics to determine the additional cost of producing one more unit of a product. In this case, the marginal cost function is expressed as 4x^3 - 80x + 700 pounds per unit.
To find the total cost function, we need to integrate the marginal cost function. Integrating 4x^3 - 80x + 700, we obtain the total cost function: C(x) = x^4 - 40x^2 + 700x + C, where C is the constant of integration.
Given that the total cost of producing the first 4 units is 1300 pounds, we can solve for C by substituting the values of x and C into the total cost function equation. After finding C, we can finalize the total cost function.
To determine the total cost of producing 7 units, we simply substitute x=7 into the total cost function and calculate the result. This will give us the specific cost associated with producing 7 units.
