The following is a linear programming model for analyzing the product mix of Maxine's Hat Company, which produces three hat types: Maximize: Z = $7X* $8X, * $6X, Subject to: 2X, +4X, 2X, 5120 (machine A time) 5X, +3X, 2X, 5400 (machine B time) 2X, + 2X, +4X, 5110 (machine C time) X 20, X, 20, and X, 20 The POM for Windows printout below shows the optimal solution to the problem. (a) Results Screen X RHS Shadow Price 8 X, 7 2 0.15 50 Maximize Machine A Machine B Machine Solution & 4 0.05 0.10 5 6 2 0.10 0.10 0 120 400 110 390 0.5 0 3 (b) Ranging screen Upper Bound Variable Value Reduced Cost X1 50 X2 5 X3 0 7 Constraint Shadow Price Slack/Surplus Machine A .5 0 Machines 0 135 Machine C 3 0 Original Val 7 8 6 Original Val Lower Bound 4.6667 7 -Infinity Lower Bound 110 265 60 14 13 Upper Bound 120 220 400 110 Infinity 120 Consider each of the following statements independently, and state whether it is true or false. Explain each answer. con now Pnce U unnar va Lower bound upper bound Machine A 5 0 120 110 220 Machine B 0 135 400 205 Machine C 3 0 110 00 120 Consider each of the following statements independently and state whether is true or false Explainench new the price of hat 3 were increased to $11.75, it would be part of the optimal product mix. (Het Hat 3 is represented by X, and is primal value currently in which means that it is not to be produced O A True, because the reduced cost of Hat 3 is $7.00 OB. Fale, because the optimal value of Hat I would remain at is current and its price or above $13.00 O C. True, because the price of Hat increased more than 50% of current prin OD Unknown, because the optimal value of at should be recalculated with the new sing prin b. The capacity of machine B can be reduced to 300 hours without affecting profits. O A True, because the new limit is lower than is previous value OB. True, because the new RHS value is within the range in which the shadow price of Owould remain vald OC Fase, because the new limit is lower than its previous value and its shadow price would change OD False because the new limit is lower than its previous valcontraint would become more restrictive c. It machine Chas a capacity of 115 hours, the production of it would remain unchanged O A True, because the new RHS value is within the range in which the dew price of a would remain vold OB. False, because the new Imit is higher than its previous value and its shadow price would change OC False, because constraint C is a birding constraint OD. True, because the new limit is higher than its previous value and the contraint would become less restrictive Click to select your