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Question

A soccer club wants to create an experienced team and need to organise an event to run a series of trials.

The teams combination is to include experienced soccer players (d ) and training analysts (t ).

The team is no more than 8 people. At least 1 analyst and 3 but no more than 6 soccer players.

The number of soccer players must be greater than the number of analysts.

A minimum of 18 trials need to be conducted on the development of the new team per day.

Soccer players are able to view the trials 5 times per day and analysts only 3.

Soccer players are paid $450 per day.

Analysts are paid $250 per day.

Questions:

1. Organisers want to run this event at a minimum expense, express the objective function.
2. Express the constraints to which the function is subject to a system of inequalities. 
3. Find the corner points of the feasible region.
4. How many soccer players & analysts should be chosen for the team.

Answer 1

1. The objective function is P = 450d + 250t

2. d+t < 8

t > 1

3<d<6

d>t

5d+3t>18

3. By graphing the system of inequalities given by the constraints, we see that the corner points (d,t) of the feasible region are (3,1), (6,2), and (6,1).

4. P(3,1) = 1600, P(6,2) = 3200, P(6,1) = 2950. The minimum value of the objective function here is 1600, and it occurs when d=3 and t=1. Therefore, 3 soccer players and 1 analyst should be chosen for the team.