Formulate (but do not solve) an algebraic model for the following situation.

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 $10 per kilogram (kg). Each swing requires 32 kg of metal, while each slide requires 8 kg. Each product spends time in three operations: cutting; polishing; and assembly. The times in minutes per unit are:

	cutting	polishing	assembly
swing	50	13	17
slide	20	11	12

Each day, the shop is available for six hours of productive time. There are four cutting machines, one polisher, and one person to do the assembly. The rust-proofing firm charges $90 per hour. When rust- proofing swings, they can rust-proof 8 swings per hour; when rust-proofing slides, they can rust-proof 20 slides per hour. The metalworking company sells its products to a wholesaler at $400 per swing and $280 per slide. The market requires that at most three slides be made for every swing made. We define (all variables are on a daily basis)

S=the number of swings made L=the number of slides made R=the number of hours of rust-proofing purchased

M=the number of kilograms of metal purchased