(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.

5. A metalworking company buys sheet metal from which they make swings and slides for children's 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: Swing Slide Cutting Polishing Assembly 25 12 16 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 rust- proof 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 L R M A = = the number of swings made (integer) the number of slides made (integer) the number of hours of rust-proofing purchased the number of kilograms of metal purchased the number of extra assembly minutes purchased