Question 2 (80 Points Total): Frieda Peeples has just got off the phone with Halley Tosis. Halley called her because she needed to source two different kinds of mint leaves for her new gum that she is going to sell. Frieda Peeples is excited about Nomask gum because it will allow her to utilize 17 new greenhouses that she has just built for producing mint. These greenhouses each has a cost of $31,500 to use each one. Frieda also has a fixed cost of production which includes utilities, land mortgage, management, and other miscellaneous fixed costs of $78,500. Each greenhouse has the capability of producing many types of mints including Apple Mint and Spearmint. While each greenhouse can produce each type of mint, there are some inefficiencies that occur by utilizing more greenhouses to produce more of the same kind of mint. Frieda estimates that the production function for Apple Mint can be represented as: A=f(G,)=840G,>", where A represents the number of 5-pound boxes that can be produced of Apple Mint and Ga represents the number of greenhouses used to produce Apple Mint. To produce Spearmint, Frieda believes the production function can be represented as: S=f(Gs)=1200G,>%, where S represents the number of 5-pound boxes that can be produced of Spearmint and Gs represents the number of greenhouses used to produce Spearmint. Frieda and Halley came to an agreement that Halley would pay $70 for a 5-pound box of Spearmint and $50 for a 5-pound box of Apple Mint. Assuming Frieda's goal is to maximize profit given the 17 greenhouses she has available for producing Apple mint and Spearmint, please answer the following questions: A. What is the optimal profit at the optimal solution? If you solve this problem using MVP's, you will lose 10 points. (40 Points) B. Graph the optimal solution. Be sure to use revenue rather than profit when you are graphing the optimal solution. (30 Points) C. Suppose Halley is willing to increase the price she pays for Spearmint to $105 per 5- pound box. How much should Frieda ask from Halley for a 5-pound box of Apple Mint so that Frieda's optimal production decision does not have to change? Please explain. (10 Points) Step 1: Define the Problem Clearly Frieda Peeples has 17 greenhouses and needs to decide how to allocate these greenhouses between producing Apple Mint and Spearmint to maximize her profit. The two types of mint have production functions that describe how many 5-pound boxes can be produced, based on the number of greenhouses allocated to each type. * Apple Mint Production Function: A= f(G,) = 8406" Where: Ais the number of 5-pound boxes of Apple Mint produced. G, is the number of greenhouses used for Apple Mint production. * Spearmint Production Function: S = f(Gs) = 12006," Where: Sis the number of 5-pound boxes of Spearmint produced. Gg is the number of greenhouses used for Spearmint production. Step 2: Revenue Function The revenue Frieda earns from selling Apple Mint and Spearmint is based on the price she receives for each type of mint. According to the problem: Apple Mint is sold for $50 per 5-pound box. Spearmint is sold for $70 per 5-pound box. The total revenue is the sum of the revenue from Apple Mint and Spearmint, so: Revenue = 50A + 70S Substitute the production functions for A and S: Revenue = 50(840G"/*) + 70(1200G*, *) Revenue = 42000G";* + 84000," Step 3: Constraint We know from the problem that Frieda has 17 greenhouses in total, and she needs to allocate them between Apple Mint and Spearmint production. The constraint is: Guat+Gs