Question 2 (20 marks: The LINDO output for the linear programming model in Table 1 represents a problem whose solution will tell a specialty retailer how many of four different styles of baby cookies to stock in order to maximize profit. It is assumed that all stocked baby cookies will be sold. The variables, X, X, X, X measure the number of different brands of baby cookies: baby natura, double happiness, apple monkey, and mam mamm, respectively. The constraints are listed as storage space in units, special display racks, demand and a marketing restriction, respectively. MAX 4X: +6X: +5X: +3.5X SUBJECT TO 2) X: + 3X: + 3X: + X: 120 3) 1.5X: +2X: 334 4) 2X: + Xs+X4572 5) X: +X 12 ROW 2 3 4 CURRENT RHS 120.000000 54.000000 72.000000 12.000000 RIGHTHAND SIDE RANGES ALLOWABLE ALLOWABLE INCREASE DECREASE 48.000000 24.000000 INFINITY 36.000000 24.000000 48.000000 12.000000 12.000000 Table 1: LINDO Output OBJECTIVE FUNCTION VALUE 1) 318.00000 VARIABLE X X: X VALUE 12.000000 000000 12.000000 60.000000 REDUCED COST 000000 500000 000000 ,000000 *** ROW 2) 3) 4) 5) SLACK OR SURPLUS .000000 36,000000 000000 .000000 DUAL PRICE 2.000000 .000000 1 500000 -2.500000 By: SW Choon BOP 2024 Principles of Operation Research Trimester 2, 2021 2022 RANGES IN WHICH THE BASIS IS UNCHANGED: OBJ. COEFFICIENT RANGES REDUCED COST .000000 500000 .000000 .000000 VARIABLE VALUE X 12.000000 X: .000000 X 12.000000 X 60.000000 ROW SLACK OR SURPLUS 2) .000000 3) 36,000000 4) ,000000 .000000 DUAL PRICE 2.000000 .000000 1.500000 -2.500000 By: Sw Choon BOP2024 Principles or Operation Research Trimester 2, 2021/2022 RANGES IN WHICH THE BASIS IS UNCHANGED: OBJ. COEFFICIENT RANGES VARIABLE CURRENT ALLOWABLE ALLOWABLE COEFFICIENT INCREASE DECREASE X 4.000000 1.000000 2.500000 X 6.000000 500000 INFINITY X 5.000000 2.500000 500000 X 3.500000 INFINITY 500000 Use the LINDO output in Table I to answer the following questions i) How many baby natura baby cookies should be stocked? (2 marks) ii) How many apple monkey baby cookies should be stocked? (2 marks) How much space is left unused? (2 marks) iv) How many racks are used? (2 marks) v) By how much is the marketing restriction exceeded? (2 marks) vi) What is the total profit? (2 marks) By how much can the profit on baby natura baby cookies increase before the solution would change? (2 marks) viii) To what value can the profit on double happiness baby cookies increase before the solution would change? (2 marks) ix) By how much can the amount of space increase before there is a change in the dual price? (2 marks) x) You are offered an advertisement that should increase the demand constraint from 72 to 86 for a total cost of $20. Would you say yes, or no? (2 marks) vii)