Consider a scenario where a manufacturer creates widgets using a production function as represented by$$$$Y$=3\mathrm{.}00$L$0\mathrm{.}70$K$0\mathrm{.}50,$ where Y is widget output in thousands, L is the number of hours of labor employed, and K is the number of hours that the production machinery is in use. Additionally, let's assume that the firm has contracted$50\mathrm{.}00$ hours of machine time rented at a cost of $$12\mathrm{.}15$ per hour. The widgets can be sold at a rate of $$50\mathrm{.}00$ per thousand widgets, and the manufacturer pays its workers a wage of $$18\mathrm{.}18$ per hour.

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$1$st attempt

Part $1(1\mathrm{.}7$points$)$

See Hint

How many hours of labor should the manufacturer hire to maximize profit? $($Do not$$round until your final answer, then round to two decimal places.$)$

$$hours

Part $2(1\mathrm{.}7$points$)$

See Hint

How many thousands of widgets will be produced? $($Round to two decimal places.$)$

$$thousands

Part $3(1\mathrm{.}7$points$)$

See Hint

What is the level of profits earned? $($Round to two decimal places.$)$

$$$$$