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Final answer:The direct materials budget calculation for the third quarter includes determining the total snowboards needed for production, the corresponding carbon fiber requirement, and the cost of purchasing the required carbon fiber; resulting in a budget of $3,377,000.Explanation:To prepare the direct materials budget for the third quarter, we need to calculate the total materials required for production and then adjust it for the desired ending inventory. Here's how the budget is determined step by step:Total needed for production: This is the number of snowboards budgeted to be sold (157,000) plus the desired ending inventory of snowboards (4,200), minus the beginning inventory of snowboards (5,700).Total pounds of carbon fiber needed: Since each snowboard requires 1 pound of carbon fiber, the total needed for production is the same number as the total snowboards needed.Total carbon fiber to be purchased: To this figure, we add the desired ending inventory of carbon fiber (4,700 lbs) and subtract the beginning carbon fiber inventory (6,700 lbs).Total cost of carbon fiber: The amount of carbon fiber to be purchased is then multiplied by the cost per pound ($22).So, the calculation will be as follows:Total snowboards needed for production = 157,000 + 4,200 - 5,700 = 155,500Total pounds of carbon fiber needed = Total snowboards needed (since 1 pound per snowboard) = 155,500Total carbon fiber to be purchased = 155,500 + 4,700 - 6,700 = 153,500Total cost of carbon fiber = 153,500 pounds * $22/pound = $3,377,000The direct materials budget for the third quarter for carbon fiber thus amounts to $3,377,000....

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