HW Unit 3: Basics of Linear Optimization (50 points) Submit all answers via Canvas. 1. The Desk Company (30 points) The Desk Company produces two types of desks, traditional and modern. The profit that it makes from a traditional desk is $350. Its profit for each modern desk is $450. The desks are produced using three machines: a drill, a saw and a gluing machine. The hours needed by each desk on each machine are given below. Also given below is the capacity next week in terms of the number of hours available. Finally, marketing considerations require that at least 20% off the desks be traditional and that at least 30% be modern. What should The Desk Company produce? Machine Drill Traditional 1.5 Modern Hours available next week 2.0 1,000 Saw 3.0 4.5 2,000 Gluing 2.5 1.5 1,500 Hint: See Unit 3 Practice Problem #1 (a) Formulate the problem as an algebraic linear optimization model include the objective and constraint formulas. Be sure to define your variables. (Submit copy of Handwritten answer, 5 pts) (b) Construct an EXCEL model for this problem (Submit answer in an Excel file, 5 pts) (c) Optimize your EXCEL model using Solver and give the Answer and Sensitivity Reports. From the Answer Report, what is the optimal solution and the optimal profit? (Submit copy of Handwritten answer, 5 pts) (d) If the Company could get 50 more hours of Drilling capacity, should they do it? If so, how much should they be willing to pay for it? Note: Use Sensitivity Report. (Submit copy of Handwritten answer, 5 pts) (e) If instead the Company could get 50 more hours of Sawing capacity, should they do it? If so, how much should they be willing to pay for it? Note: Use Sensitivity Report (Submit copy of Handwritten answer, 5 pts) (f) If instead the gluing time on the traditional desks could be reduced from 2.5 to 2 hours per table, how much profit would the company gain by this increase in efficiency? (Submit copy of Handwritten answer, 5 pts)