Reference no: EM132691688
A factory makes two types of lock, standard and large, on a particular day.
On that day:
the maximum number of standard locks that the factory can make is 100;
the maximum number of large locks that the factory can make is 80;
the factory must make at least 60 locks in total;
the factory must make more large locks than standard locks.
Each standard lock requires 2 screws and each large lock requires 8 screws, and on that day the factory must use at least 320 screws.
On that day, the factory makes X standard locks and Y large locks. Each standard lock cost $ 1.50 to make and each large locks cost $ 3 to make. The manager of the factory wishes to minimise the cost of making locks.
a) Formulate the manager's situation as a linear programming problem?
b) Draw a suitable diagram to enable the problem to be solved graphically, indicating the feasible region and the direction of the objective line.
c) Find the values of X and Y that correspond to the minimum cost. Hence find this minimum cost.