Reference no: EM132296074

A sawmill makes two products for log-home kits: fir logs and spruce logs which can be sold at profits of $16 and $20, respectively. Each spruce log requires .4 hours of processing time on the bark peeler and 1 hour on a slab saw. Each fir log requires .5 hours on the peeler and .7 hours on the slab saw. Each log then, regardless of type, requires .3 hours on the planer. Because of maintenance requirements and labor restrictions, the bark peeler is available 10 hours per day, the slab saw 12 hours per day and the planer 14 hours per day. Bark and sawdust are byproducts of these operations. All the bark can be put through a chipper and sold in unlimited quantities to a nearby horticulture supplier. Dried fir sawdust can be directed to a similar market, at a net profit of $1.40 per processed log. Limited amounts of the spruce sawdust can be made into marketable pressed-wood products, but the rest must be destroyed. For each spruce log produced, enough sawdust (5 pounds) is generated to make 3 pressed-wood products, which after manufacturing can be sold at a unit profit of $2 per pressed-wood product. However, the market can absorb only 60 of the pressed-wood products per day and the remaining spruce sawdust must be destroyed at a cost of $0.60 per pound. The sawmill wishes to make the largest possible profit, considering the cost of destroying the unusable spruce sawdust.

Formulate a linear program for this problem. Do not solve. Define your variables before you use them. Also, describe in a few words what is your objective function and what each of your constraints represents.