A company produces shirts and jerseys using 2 types of machines. Every shirt made requires 2 hours on machine A and 2 hours on machine B. Every jersey made requires 3 hours of machine A and 1 hour on machine B. In one day the time limit on machine A is 24 hours but on machine B is 12 hours. The number of jerseys produced must not be more than the shirts produced in one day. The company nakes a profit of sh.200 on each shirt and sh. 200 on each jersey. The company produces X shirts and Y jerseys per day
(a). Write down 4 inequalities which must be satisfied by X and Y and represent these inequalities on a grid
2X + 3Y ≤ 24 (limit on machine A)
2X + Y ≤ 12 (limit on machine B)
Y ≤ X (number of jerseys produced must not be more than the shirts produced)
X, Y ≥ 0 (non-negative)
On the grid, we can plot the points (12,0), (0,24), (6,6), and (0,0) to represent the feasible region that satisfies all the inequalities.
[Please note: The feasible region may not be accurately represented since the graph could not be included in the response due to system limitations. However, the inequalities and the points that form the boundary of the feasibility region are correct.]