Question

In: Operations Management

Rutgers is planning to expand its capacity in athletic centers. They purchased a pretty big piece...

Rutgers is planning to expand its capacity in athletic centers. They purchased a pretty big piece of land, so space is not really an issue. The options that they have are four, in terms of facilities: basketball, tennis, football, and baseball. A basketball facility is expected to cost 10,000$ and should be used by around 75 people per day. A tennis facility is expected to cost 8,000$ and should be used by around 45 people per day. A football facility is expected to cost 13,000$ and should be used by around 110 people per day. Finally, a baseball facility is expected to cost 11,000$ and should be used by around 80 people per day. Although the planner (you) is free to choose as many facilities per type as he wants, there are some restrictions: football facilities should be no more than 5 and the available budget is 250,000$. The objective is to maximize the daily usage.

At the optimal solution, how many basketball facilities should be built?

A.

None of the above

B.0

C.5

D.13

Expert Solution

Decision Variables:

Let,

Number of basketball facilities = x1

Number of tennis facilities = x2

Number of football facilities = x3

Number of baseball facilities = x4

Objective Function:

The daily usage is to be maximized.

Daily usage of basketball facility = 75 people

Daily usage of tennis facility = 45 people

Daily usage of football facility = 110 people

Daily usage of baseball facility = 80 people

The objective function is:

MAXIMIZE 75*x1 + 45*x2 + 110*x3 + 80*x4

Constraints:

The total cost should not exceed the budget of $250,000

Cost of basketball facility: $10,000

Cost of tennis facility: $8,000

Cost of football facility: $13,000

Cost of baseball facility: $11,000

10000*x1 + 8000*x2 + 13000*x3 + 11000*x4 <= 250000

Number of football facilities can be maximum 5.

x3 <= 5

Negative number of facilities is not possible.

x1 >= 0

x2 >= 0

x3 >= 0

x4 >= 0

Fractional unit of facilities is also not possible.

x1 = integer

x2 = integer

x3 = integer

x4 = integer

Putting in Excel:

Solver Parameters:

Optimal Solution:

basketball	tennis	football	baseball
x1	x2	x3	x4
13	0	5	5

At the optimal solution, how many basketball facilities should be built?

Hence, Answer is: (D) 13

.

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keosha answered 1 month ago

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