LINEAR PROGRAMMING

Table mountain Corporation (Tabco) manufactures transistors. An important aspect of the manufacture of transistors is the melting of the element germanium (a major component of a transistor) in a furnace. Unfortunately, the melting process yields germanium of highly variable quality. Two methods can be used to melt germanium; method 1 costs R750 per transistor, and method 2 costs R1 050 per transistor. The qualities of germanium obtained by methods 1 and 2 are shown in a table. Grade 1 is poor while grade 4 is excellent. The quality of the germanium dictates the quality of the manufactured transistor. Tabco can refire melted germanium in an attempt to improve its quality. It costs R375 to refire the melted germanium for one transistor. The results of the re-firing process are shown in a table. Tabco has sufficient furnace capacity to melt or re-fire germanium for at most 20000 transistors per month. Tabco's monthly demands are for 1000 grade 4 transistors, 2000 grade 3 transistors, 3000 grade 2 transistors, and 3000 grade 1 transistors. Formulate an LP model to minimize the cost of producing the needed transistors