The Tubular Ride Boogie Board Company has manufacturing plan

The Tubular Ride Boogie Board Company has manufacturing plants in Tucson, AZ and Toronto, Ontario. You have been given the job of coordinating distribution of the latest model, the Gladiator, to outlets in Honolulu and Venice Beach. The Tucson plant, when operating at full capacity, 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. (

a) Assuming that you wish to fill all orders and assure full capacity production at both plants, is it possible to meet a total transportation budget of $10,500? Yes No Correct: Your answer is correct.

If so, how many Gladiator boards are shipped from each manufacturing plant to each distribution outlet? (If there is no solution, enter NONE in all answer blanks.)

Tucson to Honolulu boards

Tucson to Venice Beach boards

Toronto to Honolulu boards

Toronto to Venice Beach boards

Solution

Tucson plant capacity = 620 per week

Toronto plant capacity = 410 per week

Let number of boards Tucson to Honolulu = x

cost of transportation = $10x

and number of boards Tucson to venice = 620-x

cost of transportation = $5(620-x)

Let number of boards Toronto to Honolulu = y

cost of transportation = $20y

and number of boards Toronto to Venice = 410-y

cost of transportation = $10(410-y)

as per requirement we get

10x+5(620-x)+20y+10(410-y) =10500

5x+10y=10500-7200

x+2y=660............;;(1)

and we get boards imported in Honolulu = x+y=500

or we get boards imported in Venice = (620-x)+(410-y)=530 or x+y=500.............(2)

solving equations (!) and (2) we get x= 340 and y=160

Tucson to Honolulu boards= 340

Tucson to Venice Beach boards = 280

Toronto to Honolulu boards= 160

Toronto to Venice Beach boards = 250