Fоrmulаte the lineаr prоgrаming mоdels. DO NOT SOLVE THEM. Be sure to clearly define each decision variable and write each constraint mathematically. A bakery makes cakes and pastries, and each product needs to go through both the baking oven and the decoration station. The oven can bake 80 pastries a day if it’s used only for pastries, or 40 cakes a day if it’s used only for cakes. The decoration station can handle 60 cakes a day if it’s focused solely on cakes, or 90 pastries a day if it’s dedicated to pastries. Each cake earns the bakery $10 in profit, while each pastry brings in $5. The goal is to figure out the best daily production plan for cakes and pastries to maximize the bakery’s profits. Clearly identify: decision variables, profit-maximization objective, oven-capacity constraint, decoration-capacity constraint, non-negativity restrictions.
Fоrmulаte the lineаr prоgrаming mоdels. DO NOT SOLVE THEM. Be sure to clearly define each decision variable and write each constraint mathematically. A company makes two products P and Q using two machines A and B. Each unit of P that is produced requires 50 minutes processing time on machine A and 30 minutes processing time on machine B. Each unit of Q that is produced requires 24-minute processing time on machine A and 33 minutes processing time on machine B. Machine A is going to be available for 40 hours and machine B is available for 35 hours. Also, at most twice as much products Q must be made as products P. The profit per unit of P is $25 and the profit per unit of Q is $30. Company policy is to determine the production quantity of each product in such a way as to maximize the total profit given that the available resources should not be exceeded. In the box below, answer all of the following: Define all decision variables. Write the objective function. Write the constraint for Machine A. Write the constraint for Machine B. Write the constraint describing the required relationship between products P and Q. Include all non-negativity restrictions.
Fоrmulаte the lineаr prоgrаming mоdels. DO NOT SOLVE THEM. Be sure to clearly define each decision variable and write each constraint mathematically. Three Olympic teams and their trainers will fly back from City A to City B with a plane that can carry 100 people. Three teams are Swimming, Gymnastics and Cycling. These teams have the following number of members and trainers: Swimming 42 and 12; Gymnastics 22 and 14; Cycling 34 and 16. There must be at least one swimming trainer accompanying every three swimmers on the plane. Similarly, there must be at least one gymnastics trainer for every two gymnasts on the plane. Cyclists tend to be older and can travel by themselves without trainers. Swimming and cycling associations are equally paying for the trip and they first require that at least the 70% of the seats are allocated to swimmers, cyclists and their trainers. Second, the total number of swimmers and their trainers must equal to the total number of cyclists and their trainers. In the box below, answer all of the following: definitions of all decision variables, the objective function, if applicable, all constraints, non-negativity and any required integrality restrictions.