Glue-all Industrial produces two adhesives used in the manufacturing process for airplanes. The two adhesives, which have different bonding strength, require different amounts of production time: the IC-100 adhesive requires 20 minutes of production time per liter of finished product, and the IC-200 adhesive uses 30 minutes of production time per liter. Both products uses 1 kilo of highly perishable resin for each liter of finished product. The inventory currently holds 300 kilos of resin, and more can be obtained if necessary. However, because of the shelf life of the material, any amount not used in the next two weeks will be discarded.
The firm has existing orders for 100 liters of IC-100 and 120 liters of IC-200. Under normal conditions, the production process operates eight hours per day, five days per week.
a) Formulate the problem as a linear programming model, where Glue-all Industrial would like to achieve the highest possible profit if the profit on a liter of IC-100 is R3000, and the profit on IC-200 is R4200.