Silicon Valley Corporation (Silve) 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 $50 per transistor, and method 2 costs $70 per tran- sistor. The qualities of germanium obtained by methods 1 and 2 are shown in Table 1. Table 1 Percent Yielded by Melting Grade of Melted Germanium Method 1 Method 2 Defective 30 20 1 30 20 2 20 25 3 15 20 4 5 15 Wee: Grade 1 is part grade 4 is excellent. The quality of the secouanium dictates the quality of the manufactured transistor. Silvso can refire melted ger-manium in an attempt to improve its quality. It costs $25 to refire the melted germanium for one transistor. The results of the refiring process are shown in Table 2. Silvo has suf- ficient furnace capacity to melt or refire germanium for at most 20,000 transistors per month. Silkco's monthly de- mands are for 1.000 grade 4 transistors, 2.000 grade 3 tran- sistors. 3,000 grade 2 transistors, and 3.000 grade 1 tran- sistors. Use linear programming to minimize the cost of producing the needed transistors. Percent Yielded by refiring Defective Grade 1 Grade 2 Grade 3 Refired Grade of Germanium Defective 30 0 0 0 1 25 30 0 0 2 15 30 40 0 3 20 20 30 50 4 10 20 30 50 Silicon Valley Corporation (Silve) 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 $50 per transistor, and method 2 costs $70 per tran- sistor. The qualities of germanium obtained by methods 1 and 2 are shown in Table 1. Table 1 Percent Yielded by Melting Grade of Melted Germanium Method 1 Method 2 Defective 30 20 1 30 20 2 20 25 3 15 20 4 5 15 Wee: Grade 1 is part grade 4 is excellent. The quality of the secouanium dictates the quality of the manufactured transistor. Silvso can refire melted ger-manium in an attempt to improve its quality. It costs $25 to refire the melted germanium for one transistor. The results of the refiring process are shown in Table 2. Silvo has suf- ficient furnace capacity to melt or refire germanium for at most 20,000 transistors per month. Silkco's monthly de- mands are for 1.000 grade 4 transistors, 2.000 grade 3 tran- sistors. 3,000 grade 2 transistors, and 3.000 grade 1 tran- sistors. Use linear programming to minimize the cost of producing the needed transistors. Percent Yielded by refiring Defective Grade 1 Grade 2 Grade 3 Refired Grade of Germanium Defective 30 0 0 0 1 25 30 0 0 2 15 30 40 0 3 20 20 30 50 4 10 20 30 50