HYU manufactures two types of products (X, Y) using two types of machines (A, B). It takes 50 minutes for Machine-A and 30 minutes for Machine-B to produce Product-X. In addition, Product-Y takes 20 minutes from Machine-A and 30 minutes from Machine B. The available hours for the two machines next week were estimated to be 40 and 50 hours, respectively. In addition, "8 kg" of material is consumed in Product-X, and "2 kg" of material is consumed in Product-Y. The available amount of ingredients used next week was identified as 320kg. The estimated sales income of Product-X and Product-Y is estimated to be 50,000 won and 60,000 won, respectively. At this time, we intend to construct a production plan that can maximize sales revenue.

In addition, the marketing department predicted that product-X and product-Y would be 70 and 90 as the maximum sales expected next week. Considering next year's new product launch schedule, the production of each product cannot exceed the estimate of the maximum sales to minimize the Unsold inventory of the two products. However, due to the limitation of the product storage space, the sum of the inventory of Product-X and Product-Y cannot exceed 150.

(1) Describe the decision variables that correspond to the above problem. (Guidance: Describe the decisions that need to be drawn first, and define the variables that correspond to them)

(2) Describe all of the constraints that need to be considered in the process of solving the above problem. (Guide: First, describe each constraint in a sentence, and then express it as a formula using the variables defined in (1)

(3) Describe the object expression you want to achieve. (Guidance: First describe the object expression in a sentence, and express it as a formula using the variables defined in (1))

(4) Use the contents summarized in (1) to (3) to perform LP formulation.

(5) Graphically represent the Feasible Region configured in the corresponding problem.

(6) Use the simplex method to find the optimal solution, and then find the value of the objective function.

 

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Department Information Marketing Sales Forecast Production Available production operation capacity Material availability Purchase Distribution Storage capacity Department Information Marketing Sales Forecast Production Available production operation capacity Material availability Purchase Distribution Storage capacity

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