Question

A firm has modeled its production function, with 6 units of capital already deployed. The production...

A firm has modeled its production function, with 6 units of capital already deployed. The production function is:

q=8L-2L

The firm has also modeled its marginal profit function as:

mpq=q3-25q2+206q-560

The firm has three options as to how the quantity it can produce that can potentially maximize its profits in the short run. The firm can elect to supply 7 million units, 8 million units, or 10 million units. In other words, q=7 or q=8 or q=10.

How many widgets must the firm produce to maximize its profits and how many laborers will the firm need to employ to produce the optimal quantity?

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