Suppose we are building three types of houses: studio (S), medium (M) and large (L). Assume...

 

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Suppose we are building three types of houses: studio (S), medium (M) and large (L). Assume that, we have three types of resource constraints. Those constraints are based on labor hours, painting hours, and decoration hours. Considering the house type based profits and resources requirements with resource availabilities, you are given the linear programming model below. Besides, you are given the Excel answer and sensitivity reports. Answer the following questions by analyzing the reports MAX Z= 30S+70M+116L s.t. 2S+2.5M+3.5LS60 Labor hours 2.5S+1.5M+4Ls50 Painting hours 2S+1M+4LS40 Decoration hours S,M,L 0 Answer Report: Objective Cell (Max) Cell Name Original Value Final Value $B$10 Pofit objective: 0.00 1790.77 Variable Cells Cell Name Original Value Final Value Integer $B$7 Studio: $B$8 Medium: SB$9 Large: 0.00 0.00 Contin 0.00 15.38 Contin 0.00 6.15 Contin Constraints Cell Name Cell Value Formula Status Slack 60.00 SH$11<=$J$11 Binding 47.69 SH$12<=$J$12 Not Binding 2.307692308 40.00 SH$13<=$J$13 Binding SH$11 Labor LHS SH$12 Decoration LHS SH$13 Painting LHS Sensitivity Report Variable Cells Final Reduced Objective Allowable Allowable Cell Name Value Cost Coefficient Increase Decrease $B$7 Studio: $B$8 Medium: ŠB$9 Large: O -34.30769231 30 34.30769231 1E+30 15.38461538 70 12.85714286 41 6.153846154 116 164 18 Constraints Final Shadow Constraint Allowable Allowable Cell Name Value Price R.H. Side Increase Decrease SH$11 Labor LHS SH$12 Decoration LHS 47.69230769 SH$13 Painting LHS 60 25.23076923 60 7.5 25 50 1E+30 2.307692308 40 6.923076923 40 3.157894737 16 State the optimal number of studio, medium and large house production, and optimal profit. If the company wants to increase the available hours for one of their constraints (labor, decoration, or painting), which one they should choose? Why? Support your answer by the relevant information. State the optimality range for profit of the large house. Suppose we reduce the available capacity for labor hours by 10 hours. What can be said about the objective? Compute the new objective by using report information. Suppose we increase the profit of the medium house by $5. What can be said about the objective? Compute the new objective by using report information. Suppose we are building three types of houses: studio (S), medium (M) and large (L). Assume that, we have three types of resource constraints. Those constraints are based on labor hours, painting hours, and decoration hours. Considering the house type based profits and resources requirements with resource availabilities, you are given the linear programming model below. Besides, you are given the Excel answer and sensitivity reports. Answer the following questions by analyzing the reports MAX Z= 30S+70M+116L s.t. 2S+2.5M+3.5LS60 Labor hours 2.5S+1.5M+4Ls50 Painting hours 2S+1M+4LS40 Decoration hours S,M,L 0 Answer Report: Objective Cell (Max) Cell Name Original Value Final Value $B$10 Pofit objective: 0.00 1790.77 Variable Cells Cell Name Original Value Final Value Integer $B$7 Studio: $B$8 Medium: SB$9 Large: 0.00 0.00 Contin 0.00 15.38 Contin 0.00 6.15 Contin Constraints Cell Name Cell Value Formula Status Slack 60.00 SH$11<=$J$11 Binding 47.69 SH$12<=$J$12 Not Binding 2.307692308 40.00 SH$13<=$J$13 Binding SH$11 Labor LHS SH$12 Decoration LHS SH$13 Painting LHS Sensitivity Report Variable Cells Final Reduced Objective Allowable Allowable Cell Name Value Cost Coefficient Increase Decrease $B$7 Studio: $B$8 Medium: ŠB$9 Large: O -34.30769231 30 34.30769231 1E+30 15.38461538 70 12.85714286 41 6.153846154 116 164 18 Constraints Final Shadow Constraint Allowable Allowable Cell Name Value Price R.H. Side Increase Decrease SH$11 Labor LHS SH$12 Decoration LHS 47.69230769 SH$13 Painting LHS 60 25.23076923 60 7.5 25 50 1E+30 2.307692308 40 6.923076923 40 3.157894737 16 State the optimal number of studio, medium and large house production, and optimal profit. If the company wants to increase the available hours for one of their constraints (labor, decoration, or painting), which one they should choose? Why? Support your answer by the relevant information. State the optimality range for profit of the large house. Suppose we reduce the available capacity for labor hours by 10 hours. What can be said about the objective? Compute the new objective by using report information. Suppose we increase the profit of the medium house by $5. What can be said about the objective? Compute the new objective by using report information.

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1 The optimal number of studio house 0 The optimal number of the medium house 1538 Rounding off will ... View the full answer