Question 5 – Linear Programming 5) A tailor makes pants and sports jackets. He's a great tailor so every item of clothing that he
creates always sells out immediately,
For material he has 750 m² of cotton textile and 1000 m² of polyester. Every pair of pants (1
unit) needs 1 m² of cotton and 2 m? of polyester. Every jacket needs 1.5 m2 of cotton and 1
m? of polyester. He makes a profit of €50 on every pants he sells, and €40 on every jacket
he sells
The tailor wonders what number of pants and what number of jackets he should make in
order to maximise his profit?
(a)
Letting . = the number of pants and y = the number of jackets he should make, write
down the objective function for this problem.
(b)
Write down the constraints for this problem as a system of 4 inequalities.
(c)
What are the coordinates of the 4 points (including the point (0, 0)] that are at the 4
corners (ie, the vertices) of the 'feasible region' for this problem?
(d)
Graph the constraint inequalities, and on the graph shade in the feasible region.
What number of pants and what number of jackets should the tailor make in order to
maximise his profit?