[7-8] The Sensitivity Report for the above LP problem is given as follows, please answer the next two questions. 7. (6 pts) Given above sensitivity report, which statement is FALSE? (a) If the unit price of Product X changed to S15, the new optimal solution will still make the same optimal mix of Products X and Y, but the new optimized profit will increase $15. (b) If the unit price of Product X changed to $10, the new optimal solution will still make the same optimal mix of Products X and Y, but the new optimized profit will decrease $10. (c) If the unit price of Product X changed to 58 , the new optimal solution will change. (d) If the unit price of Product Y changed to $12, the new optimal solution will still make the same optimal mix of Products X and Y, and the optimized profit will remain the same. (e) If the unit price of Product Y changed to $14, the new optimal solution will still make the same optimal mix of Products X and Y, but the new optimized profit will inerease $40. 8. (6 pts) Given above sensitivity report, which statement is FALSE? (note: RHS stands for Right-hand side; I E+30 suggests infinity) (a) If the RHS of Material A constraint changed to 8 , the optimized profit will decrease $4. (b) If the RHS of Material B constraint changed to 15, the optimized profit will NOT change. (c) If the RHS of Material B constraint changed to 10, the optimized profit will NOT change. (d) If the RHS of Material C constraint changed to 5,5, the optimized profit will decrease $4. (c) If the RHS of Material C constraint changed to 4, the optimized profit will change. 9. (12 points) What is the optimized Z value for this following LP problem? Minimize Z=3x+10y subject to (1) 2x+4y12 and (2) 5x+2y10 and (3) x,y0. You may show your work below to earn possible partial credit