A tech company assembles and then tests two models of computers, Basic and XP$.$ For the coming month, the company wants to decide how many of each model to assemble and then test. No computers are in inventory from the previous month, and because these models are going to be changed after this month, the company doesn$$t want to hold any inventory after this month. It believes the most it can sell this month are $600$ Basics and $1200$ XPs$.$ Each Basic sells for $$300$ and each XP sells for $$450.$ The cost of component parts for a Basic is $$150$; for an XP it is $$225.$ Labor is required for assembly and testing. At most $10,000$ assembly hours and $3000$ testing hours are available. Each labor hour for assembling costs $$11$ and each labor hour for testing costs $$15.$ Each Basic requires five hours for assembling and one hour for testing, and each XP requires six hours for assembling and two hours for testing. The Tech company wants to know how many of each model it should produce $($assemble and test$)$ to maximize its net profit, but it cannot use more labor hours than are available, and it does not want to produce more than it can sell. a$.$ Write the problem above as a linear programming problem. That is outline the objective function and all the constraints. b$.$ Use Linear Programming $($Solver$)$ to find the best mix of computer models that stays within the company$$s labor availability and maximum sales constraints. c$.$ Assume there is another PC model, the VXP$,$ that the company can pro$-$ duce in addition to Basics and XPs$.$ Each VXP requires eight hours for assembling, three hours for testing, $$275$ for component parts, and sells for $$560.$ At most $50$ VXPs can be sold. i$.$ Modify the spreadsheet model to include this new product, and use Solver to find the optimal product mix. ii$.$ You should find that the optimal solution is not integer$-$valued. If you round the values in the decision variable cells to the nearest integers, is the resulting solution still feasible? $1$iii. Continuing the previous problem, perform a sensitivity analysis on the selling price of VXPs$.$ Let this price vary from $$500$ to $$650$ in increments of $$10,$ and keep track of the values in the decision vari$-$ able cells and the objective cell. Discuss your findings.