Question 1 (100 Points Total): Mandy's Candy is a small purveyor of selling unique artisanal fine chocolates. The owner, Mandy Panvirus, has had a tough time managing to stay in business over the last six months due to the global pandemic and the associated lock down of local businesses. As the holiday season arrives, Mandy's mood has been much more optimistic because she just finished a class on how to sell products over the internet. In preparation for selling her products over the internet, Mandy has just purchased a web domain name for $3,181. Mandy considers this a fixed cost of doing business online. As Mandy considers all the different types of chocolate she crafts that she can sell online, she has decided on a strategy of focusing on one specific chocolate bar that she will sell online. The purpose of focusing on one chocolate bar is so she can ensure that she can deliver whatever is demanded of her product. Being new to online selling and having a desire to obtain the highest profit possible, Mandy after doing some market research has decided to sell a single 3 oz. chocolate bar for $6. Mandy's chocolate bar has four key ingredients: almonds, nutmeg, dried fruit, and Yacon syrup. She believes that this particular chocolate bar will sell extraordinarily well online due to its unique sweetener of Yacon syrup, which comes from the roots of the Yacon plant that is native to the Andes Mountains and has a low glycemic sugar index. Mandy has spent time researching the cost of her key ingredients. She has found that a local nut grower will sell her fresh almonds for $576 per 500-pound box. She can purchase the nutmeg and dried fruit from Fruity Meg's at a cost of $36 per 12 oz. jar of nutmeg and the dried fruit for $4 per pound. Mandy has considered herself quite lucky because she has come across an online dealer who sells Yacon syrup for $9 per 5 oz. jar. Since Mandy has been making these special chocolate bars for a while, she has a very good understanding of the process to make the chocolate bars. She has a special machine that she uses for mixing the ingredients together. Her experience with this machine over the years has given her a good idea of what her production function is. Specifically, her production function can be represented by the following: C = f(A,N,D,Y) = 3(7A% + 324 + 24N) + 2(9D7T Y7 )2 (4% + N?) where C represents a single 3 oz. chocolate bar, A represents a 500-pound box of almonds, N denotes the number of 12 oz. jars of nutmeg, D represents a pound of dried fruit, and Y represents a 5-ounce jar of Yacon syrup. The expected fixed cost for the depreciation of the machine is estimated at $10,000. Please answer the following questions making sure to give proper justification: A. At the current given prices, what is the optimal amount of profit that Mandy can expect to make for producing the optimal number of chocolate bars assuming that he can sell all that she produces? (50 Points) B. Suppose that Mandy decides to not use the dried fruit or Yacon syrup. How much profit would she lose if she decided to maximize her production of chocolate bars rather than profit? (25 Points) C. Given the input prices, what is the tradeoff between almonds and nutmeg at the optimal input allocation? (15 Points) D. What is the marginal cost of production for nutmeg at the optimal input? Please explain how you got your answer. (10 Points) Question 2 (80 Points Total): Fruity Meg's has been a drier of spices and fruits for the last sixty years. Her reputation is so strong that she is known for her drying capabilities internationally. She just received a purchase order from Mandy Panvirus to purchase as much nutmeg and dried fruit that Fruity Meg's is willing to produce. The sales representative negotiated a price of $36 per 12 oz. jar of nutmeg and $4 per pound of mixed dried fruit. Fruity Meg has one large scale drier that is capable of drying both fruits and spices. This machine in a production cycle has 1,552 hours available for use in drying. The drier can be allocated to drying nutmeg and fruit in any combination of hours. The cost to operate this drier is $18 per hour and has a depreciation fixed cost of $3,808 per production cycle. Given the company's long history in drying fruits and spices, it has a very good data that was used to estimate the productivity level of the drier when it comes to drying fruits or spices. In terms of drying spices, past data indicates that a production function for drying nutmeg can be represented as 1 the following: N = f(Ty) = 4327y , where N represents the number of 12 oz. jars of nutmeg and Ty denotes the amount of hours devoted to drying nutmeg. The drier that Fruity Meg's has available is quite a bit more efficient for drying fruit. Past production data shows that the production 1 function for drying fruit can be represented as: D = f(Tp) = 115277, , where D denotes the number of pounds of dried fruit produced and Tp represents the number of hours devoted to drying a pound of dried fruit. Once the fruit and spice have been dried, they must go through the packaging machines that Fruity Meg's has. These packaging machines can handle as much fruit and spices as Fruity Meg's can produce. Since they have constant returns to scale, they do not lose or gain efficiency with more of less product being handled. The depreciation fixed cost for the spice bottler is $4,000, while the dried fruit packager has a depreciation fixed cost of $6,000. Please answer the following questions making sure to give proper justification: A. What is the optimal profit at the optimal solution for Fruity Meg's given the prices Mandy would currently like to pay? If you solve this problem using MVP's, you will lose 15 points. (50 Points) B. Graph the optimal solution. Be sure to use revenue rather than profit when you are graphing the optimal solution. (20 Points) C. If Mandy's chocolate bars are a big hit and she is willing to increase her price for dried fruit to $12, how much would the sales representative from Fruity Meg's need to increase the price of nutmeg so that the production decision for Fruity meg's does not change, i.e., they would produce the same output? Please explain. (10 Points)