3. A company makes robots, mostly for industrial use, but as a novelty item they also make robotic pets. These robotic cats and dogs are not aimed at children, but due to their high cost of production the target market is seniors, who are now in a retirement home and cannot have a living pet. One of their products is a calico cat, which is addition to meowing, can twist her head, lick her paw, and roll over onto her side. They have received orders for units of this cat six months in advance of the desired delivery. Hence the company knows that the demand over the next six months will be: January February March April May June 5200 6000 6400 4800 5100 5500 3 It is now December 1. Based on what has already been planned for this month, the inventory of this robotic cat as of December 31 will be 800 units. Up to 5000 units can be manufactured each month based on each employee working on regular time. Each cat costs $120 if manufactured on regular time. It is also possible to manufacture up to 1200 robotic calico cats per month on overtime. Each cat so produced would cost $170. Robotic pets can be kept in inventory at a cost of $5 per robot per month. This charge represents the cost of tied-up capital, warehouse, and insurance expenses. As a buffer against potentially high demand at the end of the planning horizon, the ending inventory should be at least 500 units. Shortages are permitted (except at the end of month 6), but at a penalty cost of $40 per robotic pet per month. We wish to formulate a model which seeks to minimize the sum of production costs. inventory holding costs, and shortage penalty costs.