******If you solve the models in Excel Solver, you will have to write them in standard form, i.e. all variables on the left-hand side, and a number of the right-hand side. If you use LINGO, you are not bound by this restriction. For each question, do the following: (a) Formulate an algebraic model for the problem. Submit this in Word or pdf. (b) Use the Excel Solver or LINGO to solve this model. Submit the computer file. (c) State the solution in words. Submit this in Word or pdf. When you attempt to solve these models, you might receive a message about the solution being infeasible. While this is a theoretical possibility, it wont happen for any of these questions. It means that a mistake has been made in formulating the model.*****

4. A lumber store stocks dowels in one standard length of 150 cm. Each dowel costs $20. A customer wants the store to cut him at minimal cost twenty dowels of length 67 cm, eighty dowels of length 51 cm, sixty dowels of length 28 cm, and forty dowels of length 15 cm. You might wish to use Excel to help create a list of patterns when beginning part (a).

5. A metalworking company buys sheet metal from which they make swings and slides for childrens playgrounds. They then outsource the rustproofing of the swings and slides, and sell the finished products. They buy the metal at a cost of $5 per kilogram (kg). Each swing requires 3 kg of metal, while each slide requires 6 kg. Each product spends time in three operations: cutting; polishing; and assembly. The times in minutes per unit are: Cutting Polishing Assembly Swing 25 12 16

Slide 18 10 11 Each day, the shop is available for 6.5 hours of productive time. There are four cutting machines, one polisher, and one person to do the assembly. However, up to an extra 80 minutes of assembly time can be purchased for $2 per minute. The rust-proofing firm charges $30 per hour. When rust-proofing swings, they can rustproof 5 swings per hour; when rust-proofing slides, they can rust-proof 16 slides per hour. The metalworking company sells its products to a wholesaler at $190 per swing and $75 per slide. The market requires that at least two slides be made for every swing made. We define (all variables are on a daily basis): S = the number of swings made (integer) L = the number of slides made (integer) R = the number of hours of rust-proofing purchased M = the number of kilograms of metal purchased A = the number of extra assembly minutes purchased

#Please answer both of these questions.