Donaldson, Inc. spends $79,000 a week to pay bills and maintains a lower cash balance limit of $20,000. The standard deviation of the disbursements is $10,000. The applicable weekly interest rate is.05 % and the fixed cost of transferring funds is $45. What is your cash balance target based on the Miller-Orr model?

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The Miller-Orr Model calculates the target cash balance using the formula: $Z = L + \sqrt[3]{\frac{3 \times F \times \sigma^2}{4 \times i}}$, where $Z$ is the target cash balance, $L$ is the lower limit of cash balance, $F$ is the fixed cost of transferring funds, $\sigma^2$ is the variance of cash flows, and $i$ is the interest rate.Given:- $L = $20,000$- $F = $45$- $\sigma = $10,000$ (Standard deviation, so $\sigma^2 = $10,000^2 = $100,000,000$)- $i = 0.05\% = 0.0005$ (weekly interest rate)Plugging these values into the formula:$Z = $20,000 + \sqrt[3]{\frac{3 \times 45 \times 100,000,000}{4 \times 0.0005}}$$Z = $20,000 + \sqrt[3]{\frac{135,000,000}{0.002}}$$Z = $20,000 + \sqrt[3]{67,500,000,000}$$Z \approx $20,000 + 40,897$$Z \approx $60,897$However, none of the provided options match the calculated value. Given the options, it seems there might have been a miscalculation or misunderstanding in the application of the formula or the interpretation of the options. Based on the correct application of the Miller-Orr Model and the provided options, the closest expected answer would be recalculated or reassessed, but with the given calculations and options, a direct match is not found. This suggests a need to reevaluate the calculation or the provided options.