Deus Inc. manufactures office tables and chairs in its two factories located in Luzon and Visayas....

 

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Deus Inc. manufactures office tables and chairs in its two factories located in Luzon and Visayas. Both factories produce the same two products and then sells them to wholesalers located in the respective regions. Orders from the Luzon and Visayas wholesalers will be fulfilled by the Luzon and Visayas factories, respectively. The orders from wholesalers have already been received for the next 2 months (October and November), where the number of units requested are shown below. (Deus Inc. is not obligated to completely fill these orders but will do so if it can without decreasing its profits.) Product Tables Chairs Product Tables Chairs Luzon Factory October 3,600 4,500 Product Tables Chairs Process 1 Table 1 Demand Each factory has 20 production days available in October and 23 production days available in November to produce and ship these products. Inventories are depleted at the end of September, but each factory has enough inventory capacity to hold 1,000 units total of the two products if an excess amount is produced in October for sale in November. In either factory, the cost of holding inventory in this way is P30 per unit of product 1 and P40 per unit of product 2. Each factory has the same two production processes, each of which can be used to produce either of the two products. The production cost per unit produced of each product is shown below for each process in each factory. P620 P780 Luzon Factory November 6,300 5,400 Process 1 Table 2 Costs 100 120 Process 2 P590 P850 Luzon Factory Table 3 Production Rate Visayas Factory October 4,900 5,100 Process 2 140 150 The production rate for each product (number of units produced per day devoted to that product) also is given for each process in each factory below. Visayas Factory Process 1 P610 P890 November 4,200 6,000 Process 1 Process 2 P650 P860 Visayas Factory 130 160 Process 2 110 130 The net sales revenue (selling price minus normal shipping costs) the company receives when a factory sells the products to its own customers (the wholesalers in the respective regions) is P830 per unit of product 1 and P1120 per unit of product 2. However, it also is possible (and occasionally desirable) for a factory to make a shipment to the other region to help fill the sales of the other factory. When this happens, an extra shipping cost of P90 per unit of product 1 and P70 per unit of product 2 is incurred. Management now needs to determine how much of each product should be produced by each production process in each factory during each month, as well as how much each factory should sell of each product in each month and how much each factory should ship of each product in each month to the other factory's customers. The objective is to determine which feasible plan would maximize the total profit (total net sales revenue minus the sum of the production costs, inventory costs, and extra shipping costs). Formulate a complete linear programming model that shows the individual constraints and decision variables for this problem. Solve the formulated LP model in Excel. Deus Inc. manufactures office tables and chairs in its two factories located in Luzon and Visayas. Both factories produce the same two products and then sells them to wholesalers located in the respective regions. Orders from the Luzon and Visayas wholesalers will be fulfilled by the Luzon and Visayas factories, respectively. The orders from wholesalers have already been received for the next 2 months (October and November), where the number of units requested are shown below. (Deus Inc. is not obligated to completely fill these orders but will do so if it can without decreasing its profits.) Product Tables Chairs Product Tables Chairs Luzon Factory October 3,600 4,500 Product Tables Chairs Process 1 Table 1 Demand Each factory has 20 production days available in October and 23 production days available in November to produce and ship these products. Inventories are depleted at the end of September, but each factory has enough inventory capacity to hold 1,000 units total of the two products if an excess amount is produced in October for sale in November. In either factory, the cost of holding inventory in this way is P30 per unit of product 1 and P40 per unit of product 2. Each factory has the same two production processes, each of which can be used to produce either of the two products. The production cost per unit produced of each product is shown below for each process in each factory. P620 P780 Luzon Factory November 6,300 5,400 Process 1 Table 2 Costs 100 120 Process 2 P590 P850 Luzon Factory Table 3 Production Rate Visayas Factory October 4,900 5,100 Process 2 140 150 The production rate for each product (number of units produced per day devoted to that product) also is given for each process in each factory below. Visayas Factory Process 1 P610 P890 November 4,200 6,000 Process 1 Process 2 P650 P860 Visayas Factory 130 160 Process 2 110 130 The net sales revenue (selling price minus normal shipping costs) the company receives when a factory sells the products to its own customers (the wholesalers in the respective regions) is P830 per unit of product 1 and P1120 per unit of product 2. However, it also is possible (and occasionally desirable) for a factory to make a shipment to the other region to help fill the sales of the other factory. When this happens, an extra shipping cost of P90 per unit of product 1 and P70 per unit of product 2 is incurred. Management now needs to determine how much of each product should be produced by each production process in each factory during each month, as well as how much each factory should sell of each product in each month and how much each factory should ship of each product in each month to the other factory's customers. The objective is to determine which feasible plan would maximize the total profit (total net sales revenue minus the sum of the production costs, inventory costs, and extra shipping costs). Formulate a complete linear programming model that shows the individual constraints and decision variables for this problem. Solve the formulated LP model in Excel.

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