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Reconsider the example of choosing the advertising budget for the VRX$2000$ that is presented in Section $1\mathrm{.}4.$ There it was determined that the optimal level of advertising spending was $$135,392$ leading to a profit of $$77,425.$ Now suppose that the selling price, variable cost and$/$or fixed cost can fluctuate as stated below.

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a$.$ Re$-$solve the optimization model for the VRX$2000$ using a variable cost of $$320,$ a selling price of $$400,$ and fixed costs of $$100,000.$ What are the optimal advertising budget and the resulting total profit?

b$.$ Re$-$solve the optimization model for the VRX$2000$ using a variable cost of $$280,$ a selling price of $$400,$ and fixed costs of $$100,000.$ What are the optimal advertising budget and the resulting total profit?

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Re$-$solve the optimization model for the VRX$2000$ using a variable cost of $$320,$ a selling price of $$400,$ and fixed costs of $$100,000.$ What are the optimal advertising budget and the resulting total profit?

intermediate calculations. Round your answers to the nearest whole number

$\backslash$table$[[$Advertising budget$]]$

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$\backslash$table$[[$A$,$A B$,$C$,$E$],[1$ V$,/$RX$2000$ Optimiz,zation Mode,$],[2,+,,],[3,$Parameters:,,$],[4,$Unit Variable Cost,$$320,],[5,$Unit Revenue,$$400,],[6,$Fixed Cost,$($ $$100000,],[7,,$$$100,000,],[8,,,],[8,$Decision Variable:,,$],[9,$Advertising Budget,,$],[10,,,],[11,$Prediction Formula: S$,$Sales ~~avx$+b,],[12,$a$,7\mathrm{.}01,],[13,$b$,400,],[14,,,],[15,$Expected Units Sold,,$],[16,,,],[17,,,],[18,$Total Revenue,,$],[18,$Total Variable Cost,,$],[19,$Fixed Cost,$$100,000,],[20,$Advertising Cost,,$],[21,,,],[22,$Total Profit,,$],[23,,,],[24,,,],[25,,,],[26,,,],[27,,,],[28,,,],[29,,,]]$