166 CHAPTER 3 siles and Operationg Planning This determines the values of the other problem variables. This means that the firm should firc 27 workers in January and hire 465 workers in May. The complete solution is given in Table 3-1. The total cost of this plan is (500)(465)+(1,000)(27)+(80)(1,500)=$379,500, which represents a substantial savings over both the zero inventory plan and the constant workforse plan. Note that the total inventory in column H does not include the 500 units of inventory at the start of January but does include the ending inventory of 601 units. The cost of the initia] 500 units would have been accounted for in the aggregate plan for the previous six months. The results of the linear programming analysis suggest another plan that might be more suitable for the company. Because the optimal strategy is to decrease the workforee in January and build it back up again in May, a reasonable alternative might be to not fire the 27 workers in January and to hire fewer workers in May. In this case, the most efficient method for finding the correct number of workers to hire in May is to simply re-solve the linear program, but without the variables F1,,F6, as no firing of workers means that these variables are forced to zero. (If you wish to avoid reentering the problem into the computer, simply append the old formulation with the constraints F1=0,F2=0,,F6=0.) The optimal number of workers to hire in May turns out to be 374 if no workers are fired, and the cast of the plan is approximately $386,120. This is only slightly more expensive than the optimal plan and has the important advantage of not requiring the firing of any workers. PROBLEMS FOR SECTION 3.5 24. Mr. Meadows Cookie Company makes a variety of chocolate chip cookies in the plant in Albion, Michigan. Based on orders received and forecasts of buying habits, it is estimated that the demand for the next four months is 850,1,260,510, and 980 , expressed in thousands of cookies. During a 46-day period when there were 120 workers, the company produced 1.7 million cookies. Assume that the number of workdays over the four months are respectively 26,24,20, and 16 . There are currently 100 workers employed, and there is no starting inventory of cookies. a. What is the minimum constant workforce required to meet demand over the next four months