Camel Records produces records according to Q = 4L - 0.15L².If labor costs $5 and records sell for $2,the optimal quantity of labor is:

Question

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The formula provided for Q (quantity of records produced) is Q = 4L - 0.15L². To find the optimal quantity of labor, we need to maximize Q. We can do this by taking the derivative of Q with respect to L and setting it equal to zero: dQ/dL = 4 - 0.15² = 0 0.15² = 4 ² = 26.67 We can then substitute this value back into the formula for Q to get the optimal quantity produced: Q = 4L - 26.67 To find the optimal quantity of labor, we need to solve for L when Q = R (total revenue): R = $2Q = $2(4L - 26.67) R = $8L - $53.34 $8L - $53.34 = $5L $L = 8.89 Since labor cannot be fractional, we would round down to the nearest whole number, giving us an optimal quantity of labor of 8. When we check the second derivative of Q with respect to L, we find that it is negative, confirming that this is a maximum point. However, since none of the answer choices are 8, the closest option would be 5.

Camel Records Produces Records According to Q = 4L -