Question

Save Answer Question 2 25 points BC Cruise Tours plans to buy new boats for the summer and has a budget of $420,000 for it. The boats can be purchased from two different manufacturers. BC Cruise Tours would like to purchase at least 50 boats and would like to purchase the same number from Sheerboat as from Racerboat to maintain goodwill. At the same time, BC Cruise Tours wishes to have a total seating capacity of at least 200. Pertinent data concerning the boats are summarized below. Maximum Expected Boat Builder Cost Seating Daily Profit Speedybird Sheerboat $6000 3 $ 70 Silverwings Sheerboat $7000 5 $ 80 Capsman Racerboat $5000 2 $50 Motorclass Racerboat $9000 6 $110 Formulate this problem as a linear program to maximize the daily expected profit ABC TT T Arial V 3 (12pt) VT

Answer 1

Answer 2:

Based on the information given in the question, we will formulate an LP model as mentioned below:

Decision Variables:
Let,

x1 = # No. of Speedybird Boats to be Purchased

x2 = # No. of Silverwings Boats to be Purchased

x3 = # No. of Capsman Boats to be Purchased

x4 = # No. of Motorclass Boats to be Purchased

Objective Function:

Here, an objective is to maximize the total daily expected profit, hence, the objective function:

Max Z = 70 x1 + 80 x2 + 50 x3 + 110 x4

Subject to Constraints:

C1 = 6000 x1 + 7000 x2 + 5000 x3 + 9000 x4 ≤ 420000 (Total Cost Budget)

C2 = x1 + x2 + x3 + x4 ≥ 50 (Total no. of boats should be at least 50)

C3 = x1 + x2 = x3 + x4 (No. of Boats Purchased from Sheerboat and Racerboat should be equal)

C4 = 3 x1 + 5 x2 + 2 x3 + 6 x4 ≥ 200 (Seating Capacity should be at least 200)

Non-Negativity Condition:

x1, x2, x3, x4 ≥ 0

[Note: As no specific information is given in the question, we will just formulate an LP model (i.e., No need to Solve) ]

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