Based on the information provided, it is difficult to estimate the exact budget for this contract. However, the contract is for nursing services, and the pricing will depend on the number of hours worked and the hourly rate. The contract has a base period of 6 months, with four option periods of 6 months each, and the government may issue multiple awards to satisfy the requirement for 10 registered nurses. Assuming an average hourly rate of $50-100 per hour, and an average of 1,250 hours per nurse per period, the total budget for the base period could be in the range of $62,500 to $125,000 per nurse, or $625,000 to $1,250,000 for 10 nurses. For the entire contract period, including all option periods, the total budget could be in the range of $375,000 to $750,000 per nurse, or $3,750,000 to $7,500,000 for 10 nurses.