Worded question help please

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) Your objective function are your expenses: how much you have to pay players and analysts:

y = 450 d + 250 t

(2) We're concerned how the team is composed, not about trials and views. Constraints:

(e) d + t <= 8

(f) t >= 1

(g) 3 <= d <= 6

(h) d > t

(3) The corners point come from the extreme values that we can get from the equations. Concentrate on value constraints (f), (g) instead of inequalities (e), (h)

(f) t = 1

(g) d = 3

(g) d = 6

Expand each value into the inequalities

(f) t = 1

(e) d <= 7

(g) 3 <= d <= 6

(h) d > 1

So d can vary between 3& 6, two corner points: (3,1) and (6,1)

(g) d = 3

(e) t <= 5

(f) t >= 1

(h) 3 > t (or t <= 2)

t can vary between 1 & 2, two corner points (3,1) and (3,2)

(g) d = 6

(e) t <= 2

(f) t >= 1

(h) 6 > t

t can vary between 1 & 2, two corner points (6,1) and (6,2)

All corner points: (3,1), (3,2), (6,1) and (6,2). Placing those into our objective function gives a minimum value for (3,1)