With 7 years of experience as a salesperson for a national retailer, John has decided to start his own business. He plans to sell designer clothing and has already found a convenient location in a large suburban shopping centre. The store will carry the goods of 4 well-known designers. John has decided that his inventory should not exceed $75,000. John must decide how to allocate the floor space to the 4 brands he has decided to carry. Each manufacturer requires that a minimum amount of floor space be allocated to its goods. The total surface of John's store is 3,360 square feet. The space requirements and some budgeted figures for the first year of operation are as follows: Manufacturer #1 #2 #3 #4 Minimum floor space (square feet) 500 700 600 900 Expected annual sales ($ per square foot) 300 480 450 600 Average gross margin 40% 45% 38% 35% The following are annual costs: Salaries $100,000 Rent $40 per square foot Utilities $4,500 Salaries, rent, and utilities are fixed costs. To solve his problem, John has set up the following linear program: Maximize: x (M1, M2, M3, M4) = 108M1 + 187.2M2 + 153M3 + 192M4 Subject to: M1 + M2 + M3 +M4 = 500 Minimum floor space for Manufacturer #1 M2 > = 700 Minimum floor space for Manufacturer #2 M3 > = 600 Minimum floor space for Manufacturer #3 M4 > =900 Minimum floor space for Manufacturer #4 15M1 + 22M2 + 23.25M3 + 32.50M4 =600 Binding $E$9 Square feet allocated to M#4 900 SE$9>=900 Binding $B$9 Square feet allocated to M#1 500 $B$9>=500 Binding 0 $C$9 Square feet allocated to M#2 1,105 SC$9>=700 Not binding 405 Sensitivity Report Adjustable Cells Final Reduced Objective Allowable Cell Name Value Cost Coefficient Increase $B$9 Sq.ft allocated to M#1 500 19.64 108 20 $C$9 Sq.ft.allocated to M#2 1,105 0.00 187.2 1E+30 $D$9 Sq.ft allocated to M#3 600 44.84 153 45 $E$9 Sq.ft allocated to M #4 900 84.55 192 85 Constraints Final Shadow Constraint Allowable Cell Name Value Price R.H. Side Increase $F$9 Total surface available 3,105 0 3,360 1E+30 $G$9 Maximum inventory 75,000 8.51 75 000 5,620Required: a) What is the expected contribution margin and operating income for the first year of operations? (4 Marks) b) By how much per unit and in total would the contribution margin change if the constraint on the level of inventories were set to $80,000? Explain your answer. (4 Marks) c) Would the optimal solution be the same if there was not a constraint on the level of inventories? Explain your answer, and calculate the change in contribution margin if any. (4 marks) d) Explain and define "binding" and "slack"