Carlos Butler is the production manager for the Bilco Corporation, which produces three types of spare parts for automobiles. The manufacture of each part requires processing on each of two machines, with the following processing times $($in hours$).$

Processing Time $($hours per unit$)$

Part A Part B Part C

Machine $10\mathrm{.}020\mathrm{.}030\mathrm{.}05$

Machine $20\mathrm{.}050\mathrm{.}020\mathrm{.}04$

Each machine is available $50$ hours per month. Each part manufactured will yield a unit profit as follows:

Part A Part B Part C

Unit Profit $$50$ $$40$ $$30$

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Formulate a linear programming model for this problem on a spreadsheet. Use solver to find an optimal solution.

Carlos wants to determine the mix of spare parts.

Note: Enter $"0"$ if a particular part is not produced. Round your answers to $3$ decimal places.

Determine the maximum total profit.

Note: Round your answer to $2$ decimal places.