(ii) write down the optimal solution and interpret the optimal solution

(iii) calculate the slack of surplus in each of the constrains in the above linear pro- gramming model and explain which constrain is binding and which constrain is non binding

(iv) calculate the range of optimality and the range of feasibility from the report

(v) what would happen if profit for X1 is increased from $15 to $25

(vi) what would happen if profit for X2 is decreased from $20 to $5

(vii) identify the shadow price , management is also considering decreasing the labor requiremnents from 210 to 52, will it affect the solutions explain

(3.) EcecutiveBeauty.com is an internet retailer trading with a wide range of high quality fragrance since 1999. Their mission is to provide you with premium beauty products and a choice of branded fragrance 24 hours a day. Being a pure-play internet retailer, their costs are considerably lower than High Street retailers, and are proud to pass savings on to customers by offering these products at, reasonable price. EcecutiveBeauty.com strives to ensure that the personal care products industry has the freedom to pursue creative product development and compete in a fair and responsible marketplace. Guerlain, Hugo Boss, Chanel, Giorgio Armani, Givenchy and Christian Dior are some of the brands most favored by executives. The executive manager has been assigned to develop a linear programming model to help the company to determine a product mix on one of the three production lines for EeecutiveBeauty.com, where x1,x2 and x3 represent the decision variables. MaximizeZsubjectto 5x1+6x2+4x310x1+8x2+5x34x1+2x2+5x3210200170(LABORConstraint)(SPACEConstraint)(BUDGETConstraint) x1,x2,x30. The spreadsheet solution and sensitivity report are shown in the following two tables. Table 1 Table 2 (i) Discuss in details how the values in the reduced cost columns are calculated. Specifically, we want you to calculate values of R1,R2 and R3