Question Suppose a farmer in Georgia begins to grow peaches. He uses $1,000,000 in savings to purchase land, he rents equipment for $90,000 a year, and he pays workers $130,000 in wages. In return, he produces 150,000 baskets of peaches per year, which sell for $3.00 each. Suppose the interest rate on savings is 4 percent and that the farmer could otherwise have earned $35,000 as a shoe salesman. What is the farmer's economic profit? The peach farmer earns economic profit of $ (Enter your response as an integer.) What is the farmer's accounting profit? The peach farmer earns accounting profit of $ (Enter your response as an integer.)

Firm 1 and firm 2 are Bertrand duopoloists. Firm 1 has a marginal cost of $6.00 per unit, and firm 2 has a marginal cost of $8.01 per unit. The demand for their product is p=23.00−Q, where Q is the total quantity demanded. How much does each firm sell in equilibrium? Assume that prices can only be set to the nearest cent, firms split the market if they set the same price, and there are no fixed costs. Firm 1 production:______ Firm 2 production:______ What are the profits for each firm in equilibrium? Firm 1 profit:   $______ Firm 2 profit:   $______

Problem 3 (Interruptable system logger) Design and implement a logger support the two operations wrlog() and flushlog() to manipulate the log data buffer ”logbuf” #define MAX LOG LENGTH 10 #define MAX BUFFER SLOT 5 char ∗∗ logbuf ;   int wrlog (char∗∗ logbuf , char∗ new data ); int flushlog (char∗∗ logbuf );   In this problem, there are many programs or actors that call wrlog() to append the log data to a shared buffer (i.e., log-file cache) which can be flushed to disk eventually. For simplicity, we assume the buffer contains 5 (= MAX BUFFER SLOT) data slots and the flush event occurs periodically at time out. We also assume a LOG is a fixed length string, i.e. char new log[MAX LOG LENGTH]. In practical point of view, the behavior of the system can be illustrated as a sequence of writing log data and the flush will be periodically triggered when a timeout is reached. int main() { wrlog ( data1 ); wrlog ( data1 ); wrlog ( data1 ); . . . wrlog (datan ); } In summary, the draft operations of the logger are: wrlog() append data to shared buffer but not exceed the buffer size. If it reaches the limits, it needs to wait until the buffer is flushed. flushlog() clean buffer aka. move all the stored items to somewhere (in here is printing to screen) and then delete all of them. This action runs eventually; for simplicy we just make a periodical call here. Further development: The interruptable mechanism of flush log can (further) support more unpredict events, i.e., it can handle a signall SIGUSR1, SIGUSR2 which are introduced in Lab 1 appendix. You are provided a referenced code with non-protected buffer by default, the program’s output is: $./ logbuf flushlog () wrlog (): 0 wrlog (): 1 wrlog (): 2 wrlog (): 3 wrlog (): 4 wrlog (): 7 wrlog (): 12 wrlog (): 13 wrlog (): 16 wrlog (): 17 wrlog (): 21 wrlog (): 24 wrlog (): 11 wrlog (): 26 wrlog (): 14 wrlog (): 6 wrlog (): 27 wrlog (): 28 wrlog (): 8 wrlog (): 20 wrlog (): 9 wrlog (): 22 wrlog (): 10 wrlog (): 19 wrlog (): 25 wrlog (): 29 wrlog (): 18 wrlog (): 23 wrlog (): 5 wrlog (): 15 flushlog () Slot 0: 0 Slot           1: 1 Slot           2: 2 Slot           3: 3 Slot           4: 4 Slot          5: 7 Slot              6: 12 flushlog () flushlog () flushlog () TODO: Implement the protection mechanism for wrlog() and flushlog() routines to make it a safe data accessing (to buffer). If it has a proper configuration then the program behavior is somehow like this illustration (comment out the print function name in wrlog() and flushlog() to make this clean output). $ ./ logbuf Slot           0: 0 Slot           1: 1 Slot           2: 2 Slot           3: 3 Slot           4: 4 Slot           5: 5 Slot           0: 12 Slot           1: 6 Slot           2: 7 Slot           3: 10 Slot           4: 8 Slot           5: 11 Slot           0: 17 Slot           1: 13   Slot 2: 16 Slot 3: 15 Slot 4: 14 Slot 5: 18 Slot 0: 25 Slot 1: 20 Slot 2: 19 Slot 3: 21 Slot 4: 22 Slot 5: 23 Slot 0: 27 Slot 1: 28 Slot 2: 26 Slot 3: 24 Slot 4: 29 Slot 5: 9  

(a) [10 pts) Show that the integrand (differential form belongs to the integral sign) is exact in the domain D. (21,3,7/2) s (y sin z dx + x sin z dy + xy cos z dz) (0,1,0) (b) [5 pts) Evaluate the integral in (a) by showing your works in details.

(a) [10 pts) Show that the integrand (differential form belongs to the integral sign) is exact in the domain D. (21,3,7/2) (y sin z dx + x sin z dy + xy cos z dz) (0,1,0) (b) [5 pts] Evaluate the integral in (a) by showing your works in details.

Task 1 :Here we're going to write Python code to process historical transaction data to implement the feature.Suppose that we are using a Python list to maintain all products purchased in different transactions:transactions = [[2, 8, 3, 6, 1, 9], [0, 5, 9], [0, 9], [4, 7, 0, 5, 9], [8, 3], [1, 6, 3, 8], [9, 0, 5], [3, 8], [5, 7, 0, 4], [3, 1, 2, 6, 0]]Elements in each sublist represent product IDs co-purchased in a transaction.Our goal is, for each product in this tiny transaction dataset, recommend products that are most frequently purchased together with the current product.Please complete the following tasks based on the problem description.For each transaction, enumerate all pairs of products that co-occur in the corresponding sublist. For example, processing the sublist [9, 0, 5] should produce three pairs (0, 5), (0, 9), and (5, 9).Pay attention to the order of product IDs in each pair. The same product pair (e.g., product 5 and product 9) can have two different representations (i.e., (5, 9) and (9, 5)). To facilitate the subsequent processing, make sure all pairs each are represented by its ascending representation (e.g., (0, 5) rather than (5, 0)).Moreover, make sure product pairs created from the same sublist are sorted first by the 1st element and then by the 2nd element. E.g., the list of pairs created from the sublist [1, 6, 3, 8] should be presented as [(1, 3), (1, 6), (1, 8), (3, 6), (3, 8), (6, 8)].Produce a Python list, product_pairs, whose values each are a list of such pairs.The expected output of print(product_pairs) is as follows:[[(1, 2), (1, 3), (1, 6), (1, 8), (1, 9), (2, 3), (2, 6), (2, 8), (2, 9), (3, 6), (3, 8), (3, 9), (6, 8), (6, 9), (8, 9)], [(0, 5), (0, 9), (5, 9)], [(0, 9)], [(0, 4), (0, 5), (0, 7), (0, 9), (4, 5), (4, 7), (4, 9), (5, 7), (5, 9), (7, 9)], [(3, 8)], [(1, 3), (1, 6), (1, 8), (3, 6), (3, 8), (6, 8)], [(0, 5), (0, 9), (5, 9)], [(3, 8)], [(0, 4), (0, 5), (0, 7), (4, 5), (4, 7), (5, 7)], [(0, 1), (0, 2), (0, 3), (0, 6), (1, 2), (1, 3), (1, 6), (2, 3), (2, 6), (3, 6)]] Full credits will be awarded only if your answer is a comprehension implemention. Loop implementations can only get at most 80% of full marks.Task 2 :Next, we will process product_pairs to create a dictionary cooccurences, whose keys are product pairs and whose values represent the number of their co-occurrences across transactions.The expected output of print(cooccurences) should look like the following (the output formatting can be different):{(0, 1): 1, (0, 2): 1, (0, 3): 1, (0, 4): 2, (0, 5): 4, (0, 6): 1, (0, 7): 2, (0, 9): 4, (1, 2): 2, (1, 3): 3, (1, 6): 3, (1, 8): 2, (1, 9): 1, (2, 3): 2, (2, 6): 2, (2, 8): 1, (2, 9): 1, (3, 6): 3, (3, 8): 4, (3, 9): 1, (4, 5): 2, (4, 7): 2, (4, 9): 1, (5, 7): 2, (5, 9): 3, (6, 8): 2, (6, 9): 1, (7, 9): 1, (8, 9): 1}Full credits will be awarded only if the order of keys in your result matches exactly that in the expected output.Task 3 :Process cooccurences to output a new dictionary recommendation whose entries each are a list of recommended products associated with the number of transactions where they were co-purchased.The expected output is as follows:{0: [(5, 4), (9, 4), (4, 2), (7, 2), (1, 1), (2, 1), (3, 1), (6, 1)], 1: [(3, 3), (6, 3), (2, 2), (8, 2), (0, 1), (9, 1)], 2: [(1, 2), (3, 2), (6, 2), (0, 1), (8, 1), (9, 1)], 3: [(8, 4), (1, 3), (6, 3), (2, 2), (0, 1), (9, 1)], 4: [(0, 2), (5, 2), (7, 2), (9, 1)], 5: [(0, 4), (9, 3), (4, 2), (7, 2)], 6: [(1, 3), (3, 3), (2, 2), (8, 2), (0, 1), (9, 1)], 7: [(0, 2), (4, 2), (5, 2), (9, 1)], 9: [(0, 4), (5, 3), (1, 1), (2, 1), (3, 1), (4, 1), (6, 1), (7, 1), (8, 1)], 8: [(3, 4), (1, 2), (6, 2), (2, 1), (9, 1)]}It means that, e.g., for product 5 (corresponding to the entry 5: [(0, 4), (9, 3), (4, 2), (7, 2)]), a list of products (i.e., product 0, 9, 4, and 7), each being represented by a tuple with the 1st element being the ID and the 2nd the number of transactions where it has appeared together with product 5, are recommended. The recommended products are also sorted in descending order by the the number of cooccurences with product 5 (i.e., the 2nd element of inner tuples).# starter code​transactions = [[2, 8, 3, 6, 1, 9], [0, 5, 9], [0, 9], [4, 7, 0, 5, 9], [8, 3], [1, 6, 3, 8], [9, 0, 5], [3, 8], [5, 7, 0, 4], [3, 1, 2, 6, 0]]

(a) [10 pts) Show that the integrand (differential form belongs to the integral sign) is exact in the domain D. (271,3,7/2) s (y sin z dx + x sin z dy + xy cos z dz) (0,1,0) (b) [5 pts) Evaluate the integral in (a) by showing your works in details.