Question

Canada Herschel Supply Co. is a design driven global accessories brand Based in Vancouver, and produce the following styles of backpacks: (1) Settlement , (2) Dawson, and (3) Little America. Each backpack goes through four production stages: (1) cutting and coloring, (2) assembly, (3) finishing, (4) quality and packaging. The total number of hours available in each of these departments are 630, 600, 708, an d 135, respectively.

Each Settlement Backpack requires 0.7 hours of cutting and coloring, 0.5 hours of assembly, 1 hour of finishing, and 0.1 hours of quality and packaging. The corresponding numbers for each Dawson Backpack are 1 hour, 0.83 hours, 0.67 ho urs, and 0.25 hours, respectively. Likewise, the corresponding numbers for each Little America Backpack are 1 hour, 0.67 hours, 0.9 hours, and 0.4 hours, respectively.

The sales revenues for each type of backpack are as follows: Settlement $36.05, Dawson $ 39.50 , and Little America $43.30. The material costs are: Settlement $6.25, Dawson $7.50 , and Little America $8.50. The hourly cost of labor is $10 for cutting and coloring, $6 for assembly, $9 for finishing, and $8 for quality assurance and packaging.

Based on the report answer the following questions:

i) Interpret shadow price of cutting and coloring labor hours constraint.

ii) If 15 more quality and packaging hours are made available (all other values unchanged), will the profit function also improve? If yes, by how much?

iII) For what values of the objective function coefficient for Settlement Backpack produced, does this optimal solution hold true, assuming all other value s remain the same?