Answer :
To find the total cost in an optimization problem using Excel's Solver, the firm sets up the cost and revenue functions in a spreadsheet and applies Solver to determine the optimal production level that minimizes costs or maximizes profits, with the starting value critically influencing the result.
The student's question revolves around finding the total cost using an optimization problem in Excel's Solver. In such problems, the goal is typically to minimize costs or maximize profits based on given constraints and a specified objective function. For example, if a firm has a cost function TC = 2q² +10q +50 and a price P = 40, the firm would use the Solver to find the quantity of output (q) that maximizes its profit. This profit is calculated as total revenue (P*q) minus total costs (TC).
From the provided steps, we understand that initially the firm makes $11.74 profit producing nine units. After running Solver, it's found that the cost-minimizing amounts lead to a minimum total cost of $513.39. In the case of a different problem where the price is $5/unit and the total cost function is TC = 100q, the profit formula would be set in cell B2 as =5*B1-100*SQRT(B1), and Solver would maximize this profit by adjusting the quantity (B1).
It is critical to choose a realistic starting value for the optimization variable, as an inappropriate initial value could lead Solver to an incorrect solution, highlighting the importance of understanding the economic model behind the optimization problem.
