Recall the production model: \\[ \\begin{array}{l} \\text { Max } 10 x \\\\ \\text { s.t. } \\\\ 5 x \\leq 40 \\\\ x \\geq 0 \\\\ \\end{array} \\] (a) Show the mathematical model when both products are considered simultaneously. \\[ \\operatorname{Max} \\] s.t. \\[ x \\geq 0, y \\geq 0 \\] (b) Identify the controllable and uncontrollable inputs for this model. (Select all that apply.) (i) controllable \\( x \\) \\( y \\) labor hours labor availability unit profit controllable \\( x \\) \\( y \\) labor hours labor availability unit profit (ii) uncontrollable \\( x \\) \\( y \\) 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.) No file chosen (d) What are the optimal solution values of \\( x \\) and \\( y \\) ? (Let \\( P \\) be total profit in dollars.) \\[ \\begin{array}{l} x= \\\\ y=1 \\\\ p=\\$ \\end{array} \\] (e) Is the model developed in part (a) a deterministic or a stochastic model? Explain. The uncontrollable inputs are and , so the model is