Question: Let S represent the amount of steel produced (in tons). Steel production is related to the amount of labor used (L) and the amount of capital used ( C ) by thefollowing function:S=20L0.30C0.70In this formula L represents the units of labor input and C the units of capital input. Each unit of labor costs $50, and each $100.(a) Formulate an

 Let $S$ represent the amount of steel produced $($in tons$).$ Steel production is related to the amount of labor used $(L)$ and the amount of capital used $(C)$ by the

following function:

$S=20L^{0\mathrm{.}30}{C}^{0\mathrm{.}70}$

In this formula $L$ represents the units of labor input and $C$ the units of capital input. Each unit of labor costs $$50,$ and each $$100.$

$($a$)$ Formulate an optimization problem that will determine how much labor and capital are needed in order to produce $50,000$ tons of steel at minimum cost.

If your answer is zero, enter $"0".$

$($b$)$ Solve the optimization problem you formulated in part a$.$ Hint: When using Excel Solver, start with an initial $L>0$ and $C>0.$

Do not round intermediate calculations. Round your answers to the nearest whole number.

$L=$

$C=$

Cost $=$$