Adding a second product to a production model. recall the production model from section $1\mathrm{.}3$ max $10$x s$.$t$.5$x$<40$ x$<0.$ Suppose the firm in this example isconsiders a second product that has a unit price of $$5$ and requires $2$hours of production time for each unit produced. use y as the number of units of product $2$ produced. a$.$show the mathematical model where both products are considered simultaneously. b$.$ identify the contrallable and uncontrollable inputs for this model. c$.$ what are the optimal solution value for x and y$.$ d$.$ is the model developed in part a a deterministic or scholistic model. explain.