The Tubular Ride Boogie Board Company has manufacturing plants in Tucson, Arizon
ID: 3007026 • Letter: T
Question
The Tubular Ride Boogie Board Company has manufacturing plants in Tucson, Arizona, and Toronto, Ontario. You have been given the job of coordinating distribution of the latest model, the Gladiator, to their outlets in Honolulu and Venice Beach. The Tucson plant, when operating at full capactiy, can manufacture 620 Gladiator boards per week, while the Toronto plant, beset by labor disputes, can produce only 410 boards per week. The outlet in Honolulu orders 500 Gladiator boards per week, while Venice Beach orders 530 boards per week. Transportation costs are as follows: Tucson to Honolulu: $10 per board; Tucson to Venice Beach; $5 per board; Toronto to Honolulu; $20 per board; Toronto to Venice Beach: $10 per board. Your manager has informed you that the company's total transportation budget is $6550. You realize that it may not be possible to fill all the orders, but you would like the total number of boogie boards shipped to be as large as possible. Given this, how many Gladiator boards should you order shipped from each manufacturing plant to each distribution outlet?
a) Declare variables.
Let x1=
x2=
x3=
x4=
b) State the 5 Problem constraints, objective function, and if objective function is max or min
Constraint 1:
Constraint 2:
Constraint 3:
Constraint 4:
Constraint 5:
Objective function: Max or Min?
Explanation / Answer
a> the variables.
x1 = Units made in Toronto and sent to Honolulu
x2 = Units made in Toronto sent to Venice
x3 = Units made in Tucson sent to Honolulu
x4 = Units made in Tucson sent to Venice
b>
the constraints :
the Toronto plant, beset by labor disputes, can produce only 410 boards per week
=> x1 + x2 <= 410 -------------(1)
The Tucson plant, when operating at full capactiy, can manufacture 620 Gladiator boards per week
x3 + x4 <= 620 -----------------(2)
The outlet in Honolulu orders 500 Gladiator boards per week
=> x1 + x3 <= 500 ---------------(3)
Venice Beach orders 530 boards per week
=> x2 + x4 <= 530 -----------------(4)
the objective function will be minimized as the transport cost needs to be as less as possible.
Tucson to Honolulu: $10 per board; Tucson to Venice Beach; $5 per board; Toronto to Honolulu; $20 per board; Toronto to Venice Beach: $10 per board
=> 10x3 + 5x4 + 20x1 + 10x2 <= 6550 -----------(5)
the objective function will be maximized as , we would like the total number of boogie boards shipped to be as large as possible
profit function
Z(maximize) = x1 + x2 + x3 + x4 + x5
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