DSCI 5210 model based business intelligence question

The Furniture City {FC} company makes 3 kinds of couches: {1) Standard. {2} Deluxe. and {3} Luxury styles. Each couch goes through 3 production departments: (1) Cutting and Coloring, (2) Assembly. and (3) Finishing. The total number of hours available each month in each of the above departments is ?50, 1500 and 600, respectively. The time (in hours) required by 3 departments for making each couch and the prot per couch are listed below. The company has a contract of supplying at least a total of 250 Deluxe and Luxury couches per month. Couch cutrfg and Assemblylhrs) Finishinglhrs) Prot (55) Colorlng (hrs) Standard 1.0 1.3 0.6 150 Deluxe 1.2 2.4 1.0 220 Luxury 1.5 2.7 1.4 310 The company would like to make a production plan to maximize its total prot. Dene S. D. L as the variables for the numbers of Standard, Deluxe and Luxury couches produced by the company. Then the corresponding LP model is built as follows: Max 1505 + 220 D + 310 L Subject to: 1 S + 1.2 D + 1.5 L g 750 (Cutting and Coloring) 1.3 S + 2.4 D + 2.? L g 1500 {Assembly} 0.6 S + 1.0 D + 1.4 L 5 600 (Finishing) D+ L 3 250 (contract supply)