Problem 4: Silicon Valley Corporation (Silvco) 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 transistor. The qualities of germanium obtained by methods 1 and 2 are shown in the following table: Percent Yielded by Melting Grade of Melted Germanium Method 1 Method 2 Defective 35 20 1 2 3 4 25 20 15 5 20 25 20 15 Silvo can refire melted germanium 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 the following table: Refired Grade of Germanium Defective 1 2 3 Percent Yielded by Refiring Defective Grade 1 Grade 2 Grade 3 35 0 0 0 20 35 0 0 15 30 40 0 20 30 50 10 15 30 50 20 4 Silvo has sufficient furnace capacity to melt or refire germanium for at most 20,000 transistors per month. Silvco's monthly demands are for 1,000 grade 4 transistors, 2,000 grade 3 transistors, 3,000 2 grade 2 transistors, and 3,000 grade 1 transistors. Formulate an LP to minimize the cost of producing the needed transistors Problem 4: Silicon Valley Corporation (Silvco) 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 transistor. The qualities of germanium obtained by methods 1 and 2 are shown in the following table: Percent Yielded by Melting Grade of Melted Germanium Method 1 Method 2 Defective 35 20 1 2 3 4 25 20 15 5 20 25 20 15 Silvo can refire melted germanium 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 the following table: Refired Grade of Germanium Defective 1 2 3 Percent Yielded by Refiring Defective Grade 1 Grade 2 Grade 3 35 0 0 0 20 35 0 0 15 30 40 0 20 30 50 10 15 30 50 20 4 Silvo has sufficient furnace capacity to melt or refire germanium for at most 20,000 transistors per month. Silvco's monthly demands are for 1,000 grade 4 transistors, 2,000 grade 3 transistors, 3,000 2 grade 2 transistors, and 3,000 grade 1 transistors. Formulate an LP to minimize the cost of producing the needed transistors