QUESTION 1. A company is producing four types of colognes with the brand names and codes...

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QUESTION 1. A company is producing four types of colognes with the brand names and codes as follows: Jasminium (P1), Mimosa (P2), Narcissus (P3), and Rosa (P4). Company uses 1 unit of raw material and 1 hour of laboratory work to produce 2 units of P1 or 4 units of P2, Production of P3 and P4 requires additional laboratory time and additional processing costs. Accordingly, 1 unit of P3 is produced using 1 unit of P1 and this production necessitates 1 hour of laboratory work and a processing cost of 400 TL. Similarly, 1 unit of P4 is produced using 1 unit of P2 and this production necessitates 2 hours of laboratory work and a processing cost of 400 TL. Each year, the laboratory can be used for a maximum of 600 hours. In addition, the unit cost of the raw material, which can be bought 400 units per year, is 300 TL. The unit sales prices of P1, P2, P3, and P4 colognes are 700 TL, 800 TL, 2400 and 1400 TL, respectively. a) (20 pts.) Formulate a linear programming model that will provide the annual production plan to maximize the company's profit. Define the decision variables in your model and describe the constraints of it. b) (10 pts.) Solve your model utilizing Lindo software and copy the "Reports Window" created by the software and paste it into your answer file. c) (5 pts.) Interpret your solution (on an annual basis; how many units of each cologne brand should be produced and sold, what would be the annual profit, how many hours the laboratory will be used, and how many units of raw material will be used?) QUESTION 1. A company is producing four types of colognes with the brand names and codes as follows: Jasminium (P1), Mimosa (P2), Narcissus (P3), and Rosa (P4). Company uses 1 unit of raw material and 1 hour of laboratory work to produce 2 units of P1 or 4 units of P2, Production of P3 and P4 requires additional laboratory time and additional processing costs. Accordingly, 1 unit of P3 is produced using 1 unit of P1 and this production necessitates 1 hour of laboratory work and a processing cost of 400 TL. Similarly, 1 unit of P4 is produced using 1 unit of P2 and this production necessitates 2 hours of laboratory work and a processing cost of 400 TL. Each year, the laboratory can be used for a maximum of 600 hours. In addition, the unit cost of the raw material, which can be bought 400 units per year, is 300 TL. The unit sales prices of P1, P2, P3, and P4 colognes are 700 TL, 800 TL, 2400 and 1400 TL, respectively. a) (20 pts.) Formulate a linear programming model that will provide the annual production plan to maximize the company's profit. Define the decision variables in your model and describe the constraints of it. b) (10 pts.) Solve your model utilizing Lindo software and copy the "Reports Window" created by the software and paste it into your answer file. c) (5 pts.) Interpret your solution (on an annual basis; how many units of each cologne brand should be produced and sold, what would be the annual profit, how many hours the laboratory will be used, and how many units of raw material will be used?)