A firm wants to decide on its production mix for two of its expensive products X and Y. The profit per unit of x is estimated to be LE 30,000, while the profit for unit of y is estimated to be LE10,000. Each unit of x requires 100 production hours while each unit of y requires 50 production hours and the firm has a total of 500 production hours available per week.

  1. Develop a model for this problem and find the optimal solution.
  2. Given the same production requirements, if the firm must produce at least 4 units of y, what is the optimal solution in this case?
  3. Given the same production requirements, if the max to be produced from x is 2 units, what is the optimal solution?
  4. Consider the constraints in b and c together, what is the optimal solution?

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