As part of a Schedule and Operations Plan, a space capsule manufacturing company has to work out a staffing plan. The staffing plan requires providing enough workers to meet the projected production requirements. The production manager has worked out the staffing requirements for the next 6 months: Month July August September October November December Workers required 350 375 425 400 385 315 The company estimates that hiring a new employee costs $45,000 since each new employee requires significant training and and the fitting of personalized equipment. Laying off employees generally costs $13,500, which includes a severance package. The company can also decide to keep unnecessary workers employed (in order to avoid re-training and re-fitting them), and this generally costs their regular wage of $6,500 per month. The current workforce size is 370 workers and due to contractual reasons, it cannot be smaller than 350 employees during any month. a. Develop a linear program to find the staffing plan that meets the staff requirements and minimizes workforce costs (wages, hiring and layoff costs). b. Find the minimum cost staffing plan. How many staff will need to be hired and when? How many will need to be laid off and when? c. Suppose we have 5 employees that are due to retire at the end of December. Could the com- pany offer them an early-retirement incentive? When? How much is the most the company should be willing to pay as an incentive?