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M Suppose you run a small start-up company known as Shaken Veggie, which creates artisan milkshakes that are inlsed with sumptuous roots and vegetables. Recently, the organization that runs the March Madness Tournament had a contest for an opportunity to sell your product as a vendor at each of the games. Given their theme this year, Healthy Half-Time, the organization was impressed by your incredibly tasty vegetable milkshakes and thought they would make an excellent addition to the items that get sold at the tournament. As a result of your win, the organization will provide you with marketing and operation consultants who can help you with sourcing your ingredients, pricing your product, and scaling your operation to a size that will t the venues that you will be able to sell. The rst consultant that you meet is the marketing consultant. This individual has sat down with you to get a better understanding of your products. You let the individual know that you have four main ingredients to your signature milkshake, which are asparagus, radicchio, carrots, and horseradish. Based on a couple of focus groups that the marketing consultant has conducted, she recommends that you sell your milkshakes in pint size cups that will sell for $10 per cup. After some back-and-forth, the consultant and you come up with an excellent marketing gimmick for your product; Shaken Veggie, Its Shaken Not Stirred. Hence, when you make your shakes in front of the customer, the last thing you do before you give it to them is give the concoction a quick shake in the cup. The next item that the marketing consultant helps you with is the procurement of your main variable inputs, i.e., asparagus, radicchio, carrots, and horseradish. Having called around to multiple suppliers, you have found that you can purchase a 100 pound box of asparagus for $40 and a 20 pound box of radicchio for $10 from Aspachio, who offers you the best deal on these items. The company, Putting the Carrot Before the Horse, is a specialist in producing root vegetables. You have found that this company will offer you the best deal for carrots and horseradish. Specically, they are willing to supply you with carrots for $120 per 1000 pounds and horseradish for $60 per 20 pound box. While these are your main variable inputs to production, you also have some xed inputs. The total xed cost of these inputs is 3 1,480. All other costs such as rent and utilities is free to you since you won the contest. After meeting with the marketing consultant, you next meet with the production consultant. The purpose of this individual is to help you understand how your vegetables turn into milkshakes. This individual works with you for a week to gain a better understanding of how you produce your milkshakes. From the data this individual collected, he was able to develop the following production mction: M = f(A, R, C, H) = 3(256A1'2R'/2)1l2 + 3C(40 C) + 6H(1 + H) H3; where M represents a pint cup of your award winning milkshake, A represents a 100 pound box of asparagus, R is the quantity of radicchio measured in 20 pound boxes, C represents a 1,000 pounds of carrots, and H represents a 20 pound box of horseradish. Please answer the following questions making sure to give proper justication: A) At the current given prices, what is the optimal amount of prot you expect to make for producing the optimal number of milkshakes assuming that you can sell all that you produce
