Question No. (50) The writing mark is done in the form of an essay with its typical components. The General Manager has assigned you to make a decision related to solving the problem of the large number of technical malfunctions in the machines and production lines in the company, as the information indicates that the company has lost some of its customers and the delivery dates for orders have been delayed because of this, which has affected the new competing companies that now hold 25% of the share. Market decline at the expense of a 5% decline in your company's sales. Preliminary studies indicate that the aging of equipment and machinery, poor maintenance allocations, and lack of automation and computerization have contributed to all of this. Apply the decision-making model with its sequential logical steps to this case, mentioning the details of each step in an accurate, scientific and applied manner, as in the ideal theoretical case of decision-making L*Delta*S_{9} also taking place in actual reality? What is required here is to solve the problem and make a realistic decision, as in the aforementioned case, relying on the ideal theoretical approach, and based on the reality of the situation, the nature of the problem and the market conditions, make the discussion appear realistic and reflect a real practical application facing you as a manager of the company. Do not be satisfied with the theoretical narration of the stages, but rather apply that to reality.

Question No. 2 (50) marks An operator who manufactures only two goods, x and y, wants the production manager to maximize profit and minimize cost within the limits, restrictions, and available resources. The following table shows all the relevant numbers:

Quantity consumed
x	y	working hour	1000
100	50	wood	2500
150	100	iron	500
40	20	Profit from selling each unit $
100	50	Operating cost per unit $

What is required is to show the solution steps, not just the final answers. (1) Determine the quantity of production that generates the greatest possible profit? (2) Determine the value of the greatest profit that can be achieved? (3) Determine the quantity of production that generates the lowest possible cost? (4) Determine the lowest cost value that can be achieved? (5) Draw the lines representing the constraints and their coordinates, then determine the intersection points, and determine the solution region? It is a good idea to use a drawing, solving and coordinate determination program such as GeoGebra Assistant