.For each problem, please come up with a LP formulation (decision variables, objective function, and constraints) with clearly defined decision variables, an objective function, and constraints.Problem 2. The Aviston Electronics company manufactures motors for toys and small appliances. The marketing department is predicting sales of 6,100 units of the Dynamonster motor in the next quarter. This is a new high and meeting this demand will test Avistons production capacities. A Dynamonster is assembled from three components: a shaft, base, and cage. It is clear that some of these components will have to be purchased from outside suppliers because of limited in-house capacity. The variable in-house production cost per unit is compared with the outside purchase cost in the table below:

Component Shaft Base Cage Outside Cost 1.21 2.50 1.95 Inside Cost 0.81 2.30 1.45 Aviston's plant consists of three departments. The time requirements in hours of each component in each department if manufactured in-house are summarized in the following table. The hours available for Dynamonster production are listed in the last row. Component Cutting Shaping Fabrication Department Department Department Shaft 0.04 0.06 0.04 Base 0.02 0.05 Cage 0.07 | Capacity | 820 | 820 | 0.08 0.09 | 0.06 820 Formulate the problem as a linear program to find out the minimum cost production plan (you need to be more specific in your formulation) for Aviston