For MichaelsSolutions Only
reneo.kena87
sample_chapter_13.xlsxPA 1
| c. | ||||||||||||||||||
| Decision Variables | a | b | c | d | ||||||||||||||
| Calculated values | 0.2111 | 0.53111 | 0.0976 | 0.16019 | Total | |||||||||||||
| Objective Function | 0.86 | 0.94 | 0.93 | 0.85 | 0.90772 | |||||||||||||
| Constraints | ||||||||||||||||||
| 1 | 1 | 1 | 1 | 1 | 1 | |||||||||||||
| 0.774 | -0.094 | -0.093 | -0.085 | 0.09077 | >= | 0 | ||||||||||||
| -0.086 | 0.846 | -0.093 | -0.085 | 0.40847 | >= | 0 | ||||||||||||
| -0.086 | -0.094 | 0.837 | -0.085 | 1.90E-17 | >= | 0 | ||||||||||||
| -0.086 | -0.094 | -0.093 | 0.765 | 0.04539 | >= | 0 | ||||||||||||
| 0.94 | -2.79 | 0.22693 | >= | 0 | ||||||||||||||
| 0.86 | -1.86 | -2.00E-16 | >= | 0 | ||||||||||||||
| -0.129 | -0.141 | -0.1395 | 0.7225 | 6.90E-17 | >= | 0 |
a. Let the weights be a, b, c and d to midterm, final, individual assignment and Participation respectively. Korey would like to maximize the course grade. Therefore the course grade (Maximization): =0.86a + 0.94b + 0.93c + 0.85d Restrictions to course grade working: a+b+c+d=1 The weights must be non-negative, Non negativity constraints: a, b, c, d ≥ 0 The four components for each should determine 10% of the sum of the grade at least. 0.86a ≥ 0.1 (0.86a + 0.94b + 0.93c + 0.85d) 0.86a ≥ 0.086a + 0.094b + 0.093c + 0.085d 0.774a – 0.094b – 0.093c -0.085d ≥ 0 0.94b ≥ 0.1 (0.86a + 0.94b + 0.93c + 0.85d) 0846b ≥ 0.086a + 0.094b + 0.093c + 0.085d 0.846b – 0.086a – 0.093c – 0.085d ≥ 0 0.93c ≥ 0.1 (0.86a + 0.94b + 0.93c + 0.85d) 0.93c ≥ 0.086a +0.094b +0.093c + 0.085d 0.837c – 0.086a – 0.094b – 0.085d ≥ 0 0.85d ≥ 0.1 (0.86a + 0.94b + 0.93c + 0.85d) 0.85d ≥ 0.086a + 0.094b + 0.093c + 0.085d 0.765d – 0.086a – 0.094b – 0.093c ≥ 0 Here it is three times the particular assignment grade. 0.94b ≥ 3(0.93c) 0.94b ≥ 2.79c 0.94b – 2.79c ≥ 0 Midterm grade must count at least twice as much as the individual assignment score. 0.86a ≥ 2(0.93c) 0.86a ≥ 1.86c 0.86a – 1.86c ≥ 0 The presence of the grade should be less than the 15% of the whole grade. 0.85d ≤ 0.15(0.86a + 0.94b +0.93c +0.85d) 0.85d ≤ 0.129a + 0.141b +0.1395c + 0.1275d 0.7225d – 00.129a – 0.141b – 0.1395c ≥ 0
b. The complete optimization model is Course grade (Maximization): = 0.86a + 0.94b + 0.93c + 0.85d a+b+c+d=1 0.774a – 0.094b - 0.093c – 0.085d ≥ 0 0.846b – 0.086a – 0.093c – 0.085d ≥ 0 0.837c – 0.086a – 0.094b – 0.085d ≥ 0 0.765d – 0.086a – 0.094b – 0.093c ≥ 0 0.94b – 2.79c ≥ 0 0.86a – 1.86c ≥ 0 0.7225d – 0.129a – 0.141b – 0.1395c ≥ 0
c. Therefore midterm weights should be 21%, final weights 53%, individual assignment 10%, Participation should be 16%. The maximum course grade is 90%.
PA 5
| b. | ||||
| Rosenberg Land Development | ||||
| Data | ||||
| One | Two | Three | ||
| Bedroom | Bedroom | Bedroom | ||
| Unit | Unit | Unit | ||
| 1BR | 2BR | 3BR | Available | |
| Construction cost | $450,000 | $600,000 | $750,000 | $180,000,000 |
| Total units | 325 | |||
| Profit/ unit | $45,000 | $60,000 | $75,000 | |
| Minimum | 15% | 25% | 25% | |
| Model | Total | |||
| Units Build | 40 | 67 | 162 | 270 |
| Minimum | 40 | 67 | 67 | |
| Construction cost | $18,202,247 | $40,449,438 | $121,348,315 | $180,000,000 |
| Contribution in profit | $1,820,225 | $4,044,944 | $12,134,831 | $18,000,000 |
| c. | ||||
| Model | Total | |||
| Units Build | 49 | 81 | 195 | 325 |
| Minimum | 49 | 81 | 81 | |
| Construction cost | $21,937,500 | $48,750,000 | $146,250,000 | $216,937,500 |
| Contribution in profit | $2,193,750 | $4,875,000 | $14,625,000 | $21,693,750 |
a. 1BR = number of one bedroom units produced 2BR = number of two bedroom units produced 3BR = number of three bedroom units produced Maximize Total Profit = $45,000 (1BR) + $60,000 (2BR) + $75,000 (3BR) (1BR) + (2BR) + (3BR) ≤ 325 $450,000 (1BR) $600,000 (2BR) + $750,000 (3BR) ≤ $180,000,000 (1BR) ≥ 15% ((1BR) + (2BR) + (3BR)) (2BR) ≥ 25% ((1BR) + (2BR) + (3BR)) (3BR) ≥ 25% ((1BR) + (2BR) + (3BR)) (1BR) ≥ 0 (2BR) ≥ 0 (3BR) ≥ 0
One crucial assumption is interpreting sensitivity analysis information for changes in model parameters is that all other parameters is that all other model parameters are held constant. In this case the increase in budget also reflected in the budget constraint. When we change the budget the constraint also changes. This violates the assumption. The change causes the budget constraint to become infeasible, and the solution must be adjusted to maintain feasibility.
PA 19
| Children's Theater | |||||||||||||||||||
| Show | Revenue | Cost | Minimum Number of Performances | ||||||||||||||||
| 1 | $2,217 | $968 | 32 | ||||||||||||||||
| 2 | $2,330 | $1,568 | 13 | ||||||||||||||||
| 3 | $1,993 | $755 | 23 | ||||||||||||||||
| 4 | $3,364 | $1,148 | 34 | ||||||||||||||||
| 5 | $2,868 | $1,180 | 35 | ||||||||||||||||
| 6 | $3,851 | $1,541 | 16 | ||||||||||||||||
| 7 | $1,836 | $1,359 | 21 | ||||||||||||||||
| Children's Theater | |||||||||||||||||||
| Show | Minimum Number of Performances | ||||||||||||||||||
| 1 | 32 | ||||||||||||||||||
| 2 | 13 | ||||||||||||||||||
| 3 | 23 | ||||||||||||||||||
| 4 | 34 | ||||||||||||||||||
| 5 | 35 | ||||||||||||||||||
| 6 | 16 | ||||||||||||||||||
| 7 | 21 | ||||||||||||||||||
| Decision variables | a | b | c | d | e | f | g | h | i | j | k | l | m | n | |||||
| Calculated values | 0 | 0 | 0 | 16.35 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | Total | ||||
| Objective function | 968 | 1568 | 755 | 1148 | 1180 | 1541 | 1359 | 968 | 1568 | 755 | 1148 | 1180 | 1541 | 1359 | 18769.3 | ||||
| Constraints | 1 | 1 | 0 | ||||||||||||||||
| 1 | 1 | 0 | |||||||||||||||||
| 1 | 1 | 0 | |||||||||||||||||
| 1 | 1 | 16.3496 | |||||||||||||||||
| 1 | 1 | 0 | |||||||||||||||||
| 1 | 1 | 0 | |||||||||||||||||
| 1 | 1 | 0 | |||||||||||||||||
| 1 | 1 | 1 | 1 | 1 | 1 | 1 | 16.3496 | ||||||||||||
| 1 | 1 | 1 | 1 | 1 | 0 | ||||||||||||||
| 2217 | 2330 | 1993 | 3364 | 2868 | 3851 | 1836 | 2217 | 2330 | 3364 | 2868 | 3851 | 55000 |
Decision variables: Let a,b,c,d,e,f and g be the number of shows of type show 1,2,3,4,5,6, and 7 at Kristin Marie Hall. Let h,I,j,k,l,m and n be the number of shows of type show 1,2,3,4,5,6, and 7. The objective of the Children’s Theater Company is minimizing the cost. =968a + 1568b + 755c + 1148d + 1180e + 1541f + 1359g +968h + 1568i +755j + 1148k + 1180l + 1541m + 1359n
Hence, a+h ≤ 32 b+I ≤ 13 c+j ≤ 23 d+k ≤ 34 e+l ≤ 35 f+m ≤ 16 g+n ≤ 21 The 60 performances are for the Marie Hall and Lauren Theater for 150 performances. The constraint is a+b+c+d+e+f+g ≤ 60 h+i+k+l+m ≤ 150 2217 (a+h) + 2330 (b+i) + 1993 (c) + 3364 (d+k) + 2868 (e+l) + 3851 (f+m) + 1836 (g) ≥ 55000 Non negativity constraints a,b,c,d,e,f,g,h,I,j,k,l,m and n ≥ 0
The schedule has been only show number 4 with 16.34 times needs to be performed in order to minimize the cost. The highest value of revenue is $55,000. No it is not possible to achieve $60,000.
