we let a represent the umber of units sald and P the total preft, then, with a profit ef $10 per ut, assuming that S heuns ae reuired to preduce each uit and anly 90 hour of production time are avalable per week, the follewing mathematical model defnes the total profit eamed by selling unts Max 10 at SS 90 Suppose the firm in this esample considers a second product that has a unit proft of $7 and requires 3 hours ef production tme for cech unt produced. Uey as the numter of units uf product 2 produced. Show the mathematical model when both preducts are considered simultaneeusly. Expresn your answers in terms ofond y. Maximise st. 20, v20 b. Identify the controllabie and uncontroltatie inputs for this madel Controllable input Uncontrolable inputs: E F the fowchart of the inout-output process for this medel Uncontrallable Enputs Max b. Identify the controllable and uncontrollable inputs for this model. Controllable inputs: Uncontrollable inputs: e All the flowchart of the input-output process for this model. x and y X, y and laborhour availability X, y and profit labor hours and labor-hour avalability rojcted Profit and profit, labor hoDurs and labor-hour avallabiaty heck on production dme constraint y20 Controllable Mathematical Output Model Inputs d. What are the optimal solution values of x and y? Round the answers for x and y to the nearest whole number Round the anwer for prefit t units units Profit