FORMULATE THE GOAL PROGRAMMING MODEL PLEASE

1. Suppose we have cafe in stanbul and we produce two kinds of products, cake 1 and cake 2. It requires 6 minutes to produce a cake 1 and 9 minutes to produce a cake 2. The cafe has 6000 minutes of production capacity available each week. Besides, each cake 1 requires 20 grams of sugar and 30 grams of flour. Similarly, each cake 2 requires 25 grams of sugar and 35 grams of flour. Weekly available sugar and flour resources are 15000 grams and 20000 grams, respectively. The profit is $1.20 for a cake 1 and $1.25 for a cake 2. The weekly demand is for 600 cake 1 and 500 cake 2. The cafe has set the following goals, in order of importance: (1) Achieve a profit of $400 each week. (2) Meet the demand for the products in order of magnitude of their profits. (3) Limit overtime to 500 minutes. (4) Underutilization of production capacity is undesired. (5) Avoid underutilization of flour resource. (6) Avoid overusage of sugar resource. Formulate a goal programming model to determine the number of each type of cake to produce weekly to satisfy the various goals