Question

Instructions: Use the following scenario and data for questions 1 to 10. Graff Kitchen LLC, makes two types of barbeque grills. The availability of three scarce resources limits the production of the grills. The profit contribution, resource usage per unit of each grill, and availability of the resources are given in the following table: Resource 1 2 Resource Usage Per Unit Grill 1 | Grill 2 2 3 4 2 Availability 180 200 - Profit Contribution 15 12 The decision variables used in the linear programming model are: X-Number of units of grill 1 to produce *2 - Number of units of grill 2 to produce The linear programming model and the graphic solution are given in the following Max 15x, + 12x2 2x: +3*, S 180 4x + 2x2 s 200 7x + 6x2 S 420 *%220 Feasible region Optimal solution (36,28)

Answer 1

Answer : Groff Kitchen LLC, makes two types of barbeque grills. The availability of three scarce resources limits the production of the grills. The profit contribution, resource usage per unit of each grill, and availability of the resources are given in the following table:

Solution :

Keeping C_{​​​​​​1} constant at C_{​​​​​​1} =15 , the interval for C_{​​​​​​2} in which the current optimal solution remains optimal is :

Using 2nd and 3rd constraints

15 * 2/4 ≤ C_{​​​​​​2} ≤ 15 * 6/7

15 * 1/2 ≤ C_{​​​​​​2} ≤ 15 * 90/7

Therefore, fourth option is correct answer.