Problem 3: El-Tech, a laptop manufacturer, uses its facility to produce three models of laptops: Z-Arch, A-Civil, and NCutie. The demand forecast for each model over the next 12 months is given in the attached file. Manufacturing is primarily an assembly operation, and capacity is governed by the number of people on the production line. The plant operates 25 days a month, nine hours each day. It takes 45 minutes to produce ZArch, 30 minutes to make an A-Civil, and 20 minutes to produce an N-Cutie. Each worker is paid $12 per hour with a 50 percent premium for any overtime. The plant currently has 11,000 employees. Overtime is limited to 35 hours per employee per month. The plant currently maintains 800,000Z-Arch, 1,200,000 A-Civil, and 800,000 N-Cutie. The holding cost (per month) of Z-Arch, A-Civil, and N-Cutie are \$3, \$2, and \$1, respectively. Assume no backlogs, no subcontracting, no layoffs, and no new hires. a) What is the optimum production schedule for El-Tech? b) What is the annual cost for this schedule? Hint: Use 1 for the initial value of all decision variables