Assume that a cat-food company has identified the need for a low-cost dry cat food that has sufficient nutritional value to maintain basic animal health but is sufficiently cheap to get recognized to a rapidly growing market of low-income consumers. This cat food will be marketed under the brand 'Dan CAT Foods' and manufactured from excess raw materials available on some of the other production lines. The current excess raw materials have been estimated at 200kg animal protein derivative and 1800kg of grain. Two packaging formulations are considered, one for large cat breeds and the other for small cat breeds. It is estimated that the profit on the large breed cat food will be R19 per bag and the profit on the small breed cat food will be R15 per bag. The assistance of a veterinary scientist has been obtained to ensure that the product will at least have sufficient nutritional value to maintain basic animal health. Based on this it was determined that a bag of cat food for a large breed will require 500g of animal protein derivative and 5.5kg of grain, while a bag of cat food for a small breed will require 800g of animal protein derivative and 5.2kg of grain. Because a whole new production line has to be set up, management has decided that at least 150 bags of cat food for small breeds and 300 bags of cat food for large breeds must be produced to make this production line worthwhile from a management perspective. Separately type out in full the LP model for this scenario and then use the Solver tool to solve this problem and explain the optimal solution