Recall the production model: Max $10$x st $5$x S $40$ x $0$ Suppose the firm in this example considers a second product that has a unit profit of $$5$ and requires $2$ hours of labor time for each unit produced. Use y as the number of units of second product produced. $($a$)$ Show the mathematical model when both products are considered simultaneously Max $10$x s$.$t$.$ x $20$ y $20($b$)$ Identify the controllable and uncontrollable inputs for this model. $($Select all that apply.$)(1)$ controllable Oy labor hours O labor availability unit profit $($ii$)$ uncontrollable DY labor hours labor availability unit profit $($c$)$ Draw the flowchart of the input$-$output process for this model. $($Submit a file with a maximum size of $1$ MB$.)$ Choose File No file chosen This answer has not been graded yet. $($d$)$ What are the optimal solution values of x and y$?($Let P be total profit.$)$ P$=$ $ $($e$)$ is the model developed in part $($a$)$ a deterministic or a stochastic model? Explain. The uncontrollable inputs are fixed and known so the model is deterministic