A small fabrication firm makes three basic types of components for use by other companies. Each component is processed on three machines. Total capacities (in hours) are 1,700 for machines 1; 1,300 for machine 2; and 1,600 for machine 3. The processing times are as follows: Machine 1 (C): Machine 2 (C): Machine 3 (C3): Material 1 (C): Material 2 (C5): Minimum for product (C): B2 1,000 0.25 A 0.10 A 0.05 A 28 A+ 26 B+ 18 C 12 A+ 16 B+ 9C s 0.20 B + 0.10 C 0.15 B+ 0.05 C S 0.10 B+ 0.15 C s Each component contains a different amount of two basic raw materials. Raw material 1 costs $0.15 per ounce, and raw material 2 costs $0.50 per ounce. At present, 180,000 ounces of raw material 1 and 90,000 ounces of raw material 2 are available. Component A B C 1700 1300 1600 180000 90000 Processing Time (hr) Machine 1 Machine 2 0.25 0.20 0.10 0.10 0.15 0.05 28 26 18 a. Assume that the company must make at least 1,000 units of component B, that labor costs are negligible, and that the objective is to maximize profits. Specify the objective function and constraints for the problem. Objective function: Maximize Z = 28.90 A+ 17.30 B+ 17.10 C. (Enter your responses rounded to two decimal places.) Constraints (enter your responses rounded to two decimal places): Requirements (oz/unit) Component Raw Material 1 Raw Material 2 A B C Machine 3 0.05 0.10 0.15 12 16 9 Selling Price ($/unit) 39.10 29.20 24.30 Nonnegativity: b. A linear programming software shows the optimal solution as: B = 1,000 and C= 0. What is the optimal value for A? A = (Enter your response rounded to the nearest whole number.) A 0, B 0, C 0