solve and show work

In your answers be sure to clearly define any variables and parameters. Also briefly explain the objective function and each constraint in your model. Question 1. A lighting company produces two light fixtures (products 1 and 2) that require both metal frame parts and electrical components. Management wants to determine how many units of each product to produce so as to maximize profit. For each unit of product 1, 1 unit of frame parts and 2 units of electrical components are required. For each unit of product 2, 3 units of frame parts and 2 units of electrical components are required. The company has 180 units of frame parts and 350 units of electrical components. Each unit of product 1 gives a profit of $1, and each unit of product 2 gives a profit of $2. We know from market research that the demand for product 2 is at most 40 (meaning any excess over 40 units of product 2 brings no profit). Formulate a linear programming model for this problem that maximizes profit. Question 2. A manufacturing company has discontinued the production of an unprofitable product, which has freed up excess production capacity. Management is now considering devoting this excess capacity to one or more of the three remaining products call them Products 1, 2, and 3. Each product must be processed by three machines before it can be sold call them Machines A, B, and C. The number of hours each product must be worked on by each machine is summarized in the following table, on a per unit basis: Machine | Product 1 | Product 2 | Product 3 A 8 3 4 B 6 5 0 C 4 0 3 For example, producing a single unit of Product 3 requires 5 hours of processing time on Machine A and 2 hours on Machine C. Each machine can only work on one product at a time. There is no requirement on processing orders. The available capacity of the machines is summarized in the following table: Machine | Capacity (hrs/week) A 600 B 270 C 175 The sales department says that weekly demand for products 1 and 2 is effectively unlimited, but demand for product 3 is 30 units per week. Lastly, the profits gained from selling Products 1, 2, and 3 are $50, $20, and $30 per unit. a) Formulate a linear programming model for this problem that maximizes weekly profit. b) Management wants to achieve a weekly sales target of 35 units of Product 1, 25 units of Product 2, and 20 units of Product 3. Can this be done why or why not