Problem #5 [Knapsack] You decide to travel to Seattle to sell your remaining inv

Question

Problem #5 [Knapsack] You decide to travel to Seattle to sell your remaining inventory of car parts. The weight, number in stock, and profit per item are listed in the table below. Airline regulations limit the total weight of your shipment to 214 pounds. Construct an IP that can be used to determine the maximum profit you can realize on this venture. Use appropriate software to find solutions. Describe your solution in terms of the problem description 151 68 104 transmission 62 28 seat water pump 21 7 29

Explanation / Answer

Let the number of engine be x

Let the number of transimission be y

Let the number of seat be z

Let the number of water pump be w

Constraints:

Profit function Z = 151x + 68y + 44z + 29w

Weight Constraints: 104x + 62y + 28z + 21w <= 214

Item constraints

x <= 2

y <= 4

z <= 4

w <= 7

Optimal Solution: p = 16853/52; x = 51/52, y = 0, z = 4, w = 0

Now since we want the integer answers

Hence the possible solution will be x=1,y=0,z=3,w=1

p = 151+3 * 44 + 29 = 312$

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