operations research 1

exercise

The Third Cup coffee shop offers four types of coffees: regular coffee, regular espresso, premium espresso and french vanilla. These four coffees are produced from two types of grains: regular roast and premium roast. The regular coffee must be composed of at most a 30% of premium roast, the rest being regular roast. The regular espresso must be composed of at least a 40% of premium roast, the rest being regular roast. The premium espresso must be composed of at least a 70% of premium roast, while the rest of regular roast. Finally, the french vanilla is a mix of regular espresso and of premium espresso, in a proportion that accounts for at least a 40% or premium espresso. The vanilla essence is added later in a process that is irrelevant for this planning problem. The regular and premium roasts can be bought in the market at 10$ and 12$ per kg. respectively. Third Cup estimates that for the next planning period the demands for each of the four products (in kgs of the ground grain) will be of 300,400,250 and 150 for the regular coffee, regular espresso, premium espresso and french vanilla. Pose the problem of finding the optimal production plan as a linear program