Question 3 Two college friends formed a company to make backpack type book-bags to distribute through a local bookstore. The bookstore has agreed to take a combination of four models, made in Canvas, Duck, Rip-stop Nylon and Leather. The bookstore wants no fewer than 15 and no more than 40 of any one model. The bookstore has agreed to pay the friends $30.5 for each Canvas book bag, $34.5 for each Duck- book bag, $37.5 for each Rip-stop book bag and $60.50 for each leather book bag they can deliver by the end of next week. The friends have students with sewing machines who have agreed to do the sewing for them. Some students can work on either canvas or duck, can complete a book-bag in 1.5 hours and will charge $7.00 per hour to do the work. Between them, they can commit to 90 hours of work in the next week. Another student can work on the Rip-stop fabric. He can fabricate a bag in 1.7 hours, will charge $8.00 per hour to work and can work 42.5 hours in the next week. Other students have the ability to sew leather. They each can complete a bookbag in 1.9 hours and will charge $9.00 per hour to work and together they can work 80 hours during the next week. The table below provides additional information about each pack. Canvas Duck Ripstop Leather Square Yards per Pack 2.25 2.4 2.1 2.6 Cost per Square Yard 4.5 4.25 7.65 9.45 Square Yard Available 200 350 700 550 Labour hours per bag 1.5 1.5 1.7 1.9 Labour hours available 90 42.5 80 Cost per labour hour 7 7 8 9 Labour cost per bag 10.5 10.5 13.6 17.1 Material cost per bag 10.125 10.2 16.065 24.57 Total cost per bag 20.625 20.7 29.665 41.67 Profit per bag 9.875 13.8 7.835 18.83 Let X1 =number of Canvas bags produced, X2- number of Duck bags produced, X3=number of Ripstop bags produced, X4= number of Leather bags produced Max 9.875X1+ 13.8X2 + 7.835X3 + 18.83X4 subject to 1.5X1 1.5X2 <= 90 Labour for Canvas and duck 1.7X3 <= 42.5 Labour for Ripstop 1.9X4 <= 80 Labour for Leather 2.25X1 <= 200 Material for Canvas 2.4X2 <= 350 Material for Duck 2.1X3 <= 700 Material for Rip 2.6X4 <= 550 Material for Leather X1 <= 40 Max for Canvas bags X2 <= 40 Max for Duck bags X3 <= 40 Max for Rip bags X4 <= 40 Max for Leather bags X1 >= 15 Min for Canvas bags X2 >= 15 Min for Duck bags X3 >= 15 Min for Rip bags X4 >= 15 Min for Leather bags X1, X2, X3, X4>=0 Output is below. Answer the following questions (a-i) using the output please be brief. If there are two possible answers one will suffice. Where necessary a range analysis must be shown. a) What is the optimal solution ( in words? (2 marks) b) 15 hours of labour for the ripstop bag were lost. Evaluate the effect. (3 marks) c) The bookstore now says they will buy a maximum of 42 leather bags. Should this order be entertained? Explain-( 3 marks) d) If the selling price of canvas bags went up by $3.50. Evaluate the effect? (3 marks) e) What is the situation if the bookstore wants to order 46 duck bags instead of 40 maximum? (2 marks) f) What are the allowable values within which labour for canvas and duck bags can vary without affecting the shadow price?- (2 marks) g) Is the problem degenerate? Explain! (2 marks) h) Are there alternative optima in this problem? Explain (2 marks) i) What value should be in the slack column that is given by ???? (1 mark) Microsoft Excel 12.0 Answer Report Target Cell (Max) Cell Name Original Value Final Value $F$6 profit 0 1702.575 Adjustable Cells Cell Name Original Value Final Value $B$5 Number of units Canvas 0 20 $C$5 Number of units Duck 0 40 $D$5 Number of units Ripstop 0 25

$E$5 Number of units Leather 0 40 Constraints Cell Name Cell Value Formula Status Slack $F$8 Labour for Canvas and duck 90 $F$8=$H$19 Not Binding 5 $F$20 Min for Duck bags 40 $F$20>=$H$20 Not Binding 25 $F$21 Min for Rip bags 25 $F$21>=$H$21 Not Binding 10 $F$22 Min for Leather bags 40 $F$22>=$H$22 Not Binding 25 Microsoft Excel 12.0 Sensitivity Report Adjustable Cells Final Reduced Objective Allowable Allowable Cell Name Value Cost Coefficient Increase Decrease $B$5 Number of units Canvas 20 0 9.875 3.925 9.875 $C$5 Number of units Duck 40 0 13.8 1E+30 3.925 $D$5 Number of units Ripstop 25 0 7.835 1E+30 7.835 $E$5 Number of units Leather 40 0 18.93 1E+30 18.93 Constraints Final Shadow Constraint Allowable Allowable Cell Name Value Price R.H. Side Increase Decrease $F$8 Labour for Canvas and duck 90 6.583333333 90 30 7.5 $F$9 Labour for Ripstop 42.5 4.608823529 42.5 25.5 17 $F$10 Labour for Leather 76 0 80 1E+30 4 $F$11 Material for Canvas 45 0 200 1E+30 155 $F$12 Material for Duck 96 0 350 1E+30 254 $F$13 Material for Rip 52.5 0 700 1E+30 647.5 $F$14 Material for Leather 104 0 550 1E+30 446 $F$15 Max for Canvas bags 20 0 40 1E+30 20 $F$16 Max for Duck bags 40 3.925 40 5 20 $F$17 Max for Rip bags 25 0 40 1E+30 15 $F$18 Max for Leather bags 40 18.93 40 2.105263158 25 $F$19 Min for Canvas bags 20 0 15 5 1E+30 $F$20 Min for Duck bags 40 0 15 25 1E+30 $F$21 Min for Rip bags 25 0 15 10 1E+30 $F$22 Min for Leather bags 40 0 15 25 1E+30