4. [/20 Points ] DETAILS MIMS16 3.E.025. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER A linear programming computer package is needed. \begin{tabular}{|c|c|c|c|} \hline & Cabinetmaker 1 & Cabinetmaker 2 & Cabinetmaker 3 \\ \hline Hoursrequiredtocompletealltheoakcabinets & 50 & 42 & 30 \\ \hline Hoursrequiredtocompleteallthecherrycabinets & 60 & 48 & 35 \\ \hline Hours available & 40 & 30 & 35 \\ \hline Cost per hour & $36 & $42 & $55 \\ \hline \end{tabular} only on oak cabinets. Similarly, Cabinetmaker 1 can only complete 40/60=0.67, or 67%, of the cherry cabinets if it worked only on cherry cabinets. to cabinetmaker 3.) Min s.t. hours available 1 hours available 2 hours available 3 oak cherry O1,O2,O3,C1,C2,C30 (c) If Cabinetmaker 1 has additional hours available, would the optimal solution change? Explain. Yes, each additional hour of time for cabinetmaker 1 will reduce the total cost by $5 per hour. Yes, each additional hour of time for cabinetmaker 1 will reduce the total cost by $1.75 per hour. No, cabinetmaker 1 has a slack of 37.5 hours, so increasing cabinetmaker 1 's time will not reduce costs. No, cabinetmaker 1 has a slack of 26.458 hours, so increasing cabinetmaker 1 's time will not reduce costs. (d) If Cabinetmaker 2 has additional hours available, would the optimal solution change? Explain. Yes, each additional hour of time for cabinetmaker 2 will reduce the total cost by $5 per hour. Yes, each additional hour of time for cabinetmaker 2 will reduce the total cost by $1.75 per hour. No, cabinetmaker 2 has a slack of 37.5 hours, so increasing cabinetmaker 2's time will not reduce costs. No, cabinetmaker 2 has a slack of 26.458 hours, so increasing cabinetmaker 2 's time will not reduce costs. (e) Suppose Cabinetmaker 2 reduced its cost to $38 per hour. What effect would this change have on the optimal solution? Explain. The new objective function coefficients for O2 and C2 are and , respectively. The optimal solution and has a value of $