7. (Section 3.3, Exercise 26) The Tubular Ride Boogie Board Company has manufact

Question

7. (Section 3.3, Exercise 26) The Tubular Ride Boogie Board Company has manufacturing plants in Tucson, Arizona, and Toronto, Ontario. You have been given the job of coordinating the 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 weck, 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 weck. 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: S10 per board Assuming that you wish to fill all orders and ensure full-capacity production at both plants, is it possible to meet a total transportation budget of $10,200? If so, how many Gladiator boards are shipped from each manufacturing plant to each distribution outlet? a. b. Is there a way of doing this for less money? Make up an application problem leading to the given system of equations. 0.05x + 0.25y = 22 0.15x + 0.05y 8, 24 9, x+y+z=9 3x+2y + z-14 2x+y+2z = 15

Explanation / Answer

Capacity of Tucson Plant = 620 boards per week

Capacity of Toronto Plant = 410 boards per week

Cost of transportation:

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

Order quantity: Honolulu orders 500 boards per week, while Venice Beach orders 530 boards per week

Let Tucson supply x boards per week to Honolulu, then Toronto supplies 500 x boards per week to Honolulu

Let Tucson supply y boards per week to Venice Beach, then Toronto supplies 530 y boards per week to Venice

Total transportation cost = 10x + 20(500 x) + 5y + 10(530 y)

  = 15300 10x 5y (1)

x + y < = 620

500 x + 530 y < = 410 or x + y > = 620

Taking x + y = 620

Substituting y = 620 x in eq (1) above

Total transportation cost  = 15300 10x 5(620 x)

= 15300 5x 3100

  = 12200 5x

If we take transportation cost as 10200, we get

5x = 2000 or x = 400, y = 220

Thus, we can meet the budget of $10200.

Suppose if x = 450, y = 170, then transportation cost = 9950

Thus, it is possible to do this for less money.

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