1. (15 points) A firm (Services Limited) produces shoes and tires. The production of each product requires only labor. The production function for shoes is: S = 20sz 2051 where s denotes labor devoted to shoe production. The production function for tires is: T = 30t where t denotes labor devoted to tire production. The wage rate is $11 per hour. The price of shoes is $9 per unit. The price of tires is $3 per unit. Services' factory can accommodate 60 workers and no more. Formulate the above problem as a constrained optimization problem and find how much of each product (shoes and tires) Services should produce per hour