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The production function for a company's product is P = 100L + 50k - L2 - k2, where P is the output that results from L units of labor and k units of capital

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The production function for a company's product is P = 100L + 50k - L2 - k2, where P is the output that results from L units of labor and k units of capital. The unit costs of labor and capital are 6 and 3, respectively, which makes the cost function C = 6L +3k. If the company wants the total cost of inputs to be 30, determine the greatest output possible subject to this budget constraint.