3. (30 points) You make vanilla and blueberry yogurts with fresh milk. Every day you can purchase at most 150L of fresh milk. To make IL of vanilla yogurt, you need exactly 0.75L of fresh milk. To make IL of blueberry yogurt, you need exactly 0.5L of fresh milk. Vanilla yogurt sells for $150/L, and blueberry yogurt sells for $180/L. You have committed to selling 30L of vanilla yogurt and 15L of blueberry yogurt to CityU. Your yogurt is popular in the market and current demand far exceeeds your production capacity. Any yogurt produced beyond the above requirements can be sold at your own yogurt store. You want to maximize your revenue. You construct a LP and use Solver to find the optimal solution. a. (10 points) Write down the linear program to determine the optimal production plan b. (15 points) Suppose you set up the LP model in Excel and here is the result of the sensitivity report: Variable Cells Cell Name $B$3 vanilla yogurt x1 $C$3 blueberry yogurt x2 Constraints Cell Name $D$8 Fresh Milk LHS $D$9 Supply 1 LHS $D$10 Supply 2 LHS i. ii. iii. Final Reduced Objective Allowable Allowable Value Cost Coefficient Increase Decrease 1E+30 80 30 255 0 0 Final Shadow Value Price 150 30 255 360 -120 0 150 180 Constraint Allowable Allowable Increase Decrease R.H. Side 120 1E+30 150 30 15 1E+30 160 240 120 30 1E+30 What will the production plan and revenue become if the revenue of vanilla yogurt is $160/L, instead of $150/L? Do you detect the existence of multiple optimal solutions? Suppose you find a new freah milk supplier who can provides additional 100L of fresh milk every day. How will this change the optimal revenue? c. (5 points) Suppose you want to make the blueberry flavor as a limited edition product. You decide that at most 20% of all yogurt sold in total are in blueberry flavor. Write a constraint to reflect this restriction on your production mix. Appendix. Random Number Table 52 06 50 88 53 30 10 47 99 37 66 91 35 32 00 84 57 07 37 63 28 02 74 35 24 03 29 60 74 85 90 73 59 55 17 60 82 57 68 28 05 94 03 11 27 79 90 87 92 41 09 25 36 77 69 02 36 49 71 99 32 10 75 21 95 90 94 38 97 71 72 49 98 94 90 36 06 78 23 67 89 85 29 21 25 73 69 34 85 76 96 52 62 87 49 56 59 23 78 71 72 90 57 01 98 57 31 95 33 69 27 21 11 60 95 89 68 48 50 33 50 95 17 89 34 09 93 50 44 51 13 44 34 62 64 39 55 29 30 64 49 44 30 16 62 34 51 95 26 14 57 34 56 62 31 15 40 90 82 51 74 30 35 69 36 85 01 55 92 64 09 85 85 23 08 54 17 12 80 69 24 84 92 16 49 59 88 32 18 50 90 30 36 24 50 48 61 18 27 88 21 62 69 64 48 31 12 73 45 14 46 32 13 49 66 62 74 41 81 02 01 78 82 74 97 37 45 31 94 99 02 68 00 16 16 46 13 85 86 98 92 98 84 54 33 40 42 49 27 64 89 42 66 83 14 74 27 76 03 33 11 97 59 81 72 00 64 61 13 52 74 05 82 82 93 09 96 33 52 78 13 06 28 30 94 23 37 39 30 34 87 01 74 11 46 82 59 94 25 34 32 23 17 01 58 73