$1.$ ?The company has a production budget of $2500000$ ?and maximum working hours of $700$ ?hours per day. Maximum daily demand is $200$ ?units for wall clocks, $300$ ?units for radios, $150$ ?units for toasters, and $200$ ?units for watches. The maximum profit per unit of product is $17000$ ?for wall clocks, $20000$ ?for radios, $13000$ ?for toasters, and $25000$ ?for watches. The resource requirements for production are shown in the table below.

a$.$ ?Write the Mathematical Model of the above problem for maximum profit.

b$.$ ?Determine the optimal production for maximum profit by the Simplek Method