Kala is one of the top manufacturer of ukuleles. The manufacturer produces three different types of ukuleles. Its Concert produce $6 in profit per unit; its Soprano produce $4 in profit per unit; and its Tenor produce $8 in profit per unit. Each type of ukulele passes through three manufacturing stages as a part of the entire production process. The three process centers of modelling, curing and assembly has an available production time per day of 12 hours, 14 hours and 16 hours, respectively. To produce one hundred units of Concert, the time required for the process of modelling, curing and assembly is 2 hours, 3 hours and 2 hours, respectively. To produce one hundred units of Soprano, 2 hours of modelling, 2 hours of curing and 1 hour of assembly is required. Whereas 4 hours of modelling, 2 hours of curing and 2 hours of assembly is required to produce one hundred units of Tenor. Sensitivity report of the problem is given as below where C= unit of Concert to be produced each day, S = unit of Soprano to be produced each day and T = unit of Tenor to be produced each day. Variable Cells Final Reduced Objective Allowable Allowable Cell Name Value Cost Coefficient Increase Decrease $B$6 Value C 400 6. $C$6 Value S -1 4 1 1E+30 $D$6 Value T 100 8 4 4 Constraints Final Shadow Constraint Allowable Allowable Cell Name Value Price R.H. Side Increase Decrease $B$10 Modelling (LHS) $B$11 Curing (LHS) $B$12 Assembly (LHS) 12 150 12 16 2.666666667 14 100 14 4 8 10 16 1E+30 (a) Formulate a linear programming model to determine the optimum product mix for each day's production, assuming all ukuleles are sold. (b) What is the optimal solution and the value of optimal solution? (c) Suppose the number of modelling hours per day increases from 12 to 13. How much does the profit increase? Explain. (d) Suppose the number of assembly hours per day increases from 16 to 17. How much does the profit increase? Explain. (e) Which constraints are binding at the optimal solution and which is not? Explain. (f) Suppose the profit contribution of a unit of Concert is increased to $9, a unit of Soprano remains as $4 and a unit of Tenor is decreased by $2. Using 100 percent rule, determine whether the optimal solution remains, and compute the total profit contribution if the optimal solution ramaine