Estimating the budget for this contract is challenging without knowing the exact prices of the bulk gases. However, based on the estimated annual quantities of the gases, we can make an educated guess. The total estimated annual quantity of liquid nitrogen is 239,868 cubic feet, liquid oxygen is 31,680 cubic feet, and liquid carbon dioxide is 141,813 pounds. Assuming an average price of $0.50 per cubic foot for nitrogen, $1.00 per cubic foot for oxygen, and $0.25 per pound for carbon dioxide, the total annual cost would be approximately $239,868 * $0.50 = $119,934 for nitrogen, $31,680 * $1.00 = $31,680 for oxygen, and $141,813 * $0.25 = $35,453 for carbon dioxide. This gives us a total estimated annual cost of $187,067. Over the five-year period of performance, the total estimated cost would be $935,335. Therefore, the budget estimation for this contract is between $500,000 and $1,500,000.