A product mix problem

Two-Tech Inc. is a small manufacturing firm and produces two microwave components, known as Component A and Component B. The profit per unit of the Component A is $19, whereas the profit per unit of Component B is $29. Because of contractual commitments, Two-Tech must manufacture at least 25 units of Component A per week, and based on the present demand for its products, it can sell all that it can manufacture. However, it wishes to maximize profit while operating the production department within the following availability of hours in the Assembly and Testing departments: Assembly hours: 241 hours available per week Testing hours: 141 hours available per week Component A requires 4 hours of assembly and 1 hour of testing, while Component Brequires 3 hours and 2 hours, respectively The problem is to determine the optimal number each component to manufacture based on the limited resources available. The decision variables directly under Two-Tech's control are: Xi: amount of Component A manufactured per week Xa: amount of Component B manufactured per week Formulate and explain the mathematical model for this LP problem, including: a. The Objective Function b. All the constraints that the solution must satisfy, including nonnegativity Extra Points Opportunity You are only required to formulate the LP problem, however if you solve the problem by the two methods listed below you will get extra points: Graphical method - 1 point (extra) MS Excel Solver - 1 point (extra)