Directions:  Each of the questions or incomplete statements below is followed by four suggested answers or completions; select the one that is best in each case.

Antibody structure.jpg Use the above figure to match the following: Heavy Chain

The function of the _____ is to promote the maturation of T lymphocytes through the secretion of thymopoietin and thymosins.

Which of the following cells is the most critical cell in adaptive immunity?

_____ are specialized lymph capillaries that occur in the fingerlike projections (villi) that extend into the small intestine.

Lymphoid tissue that appears as a swelling of the mucosa in the oral cavity is called a(n) _____.

Farmer’s Fridge is also carrying out another experiment at it’s NYU Dance fridge.  There, the company hopes to gain insights into the extent to which packaging influences sales.  The company stocked the fridge with only the Greek Salad and on during the night of the 5th day replenished the fridge with 100 units. Table 1 documents daily sales and inventory over the subsequent 15 days with the original packaging. Table 2 documents daily sales and inventory with the new packaging.  [Start Selection] Table 1: Daily sales and inventory with the original packaging Day Inventory Sales 1 100 22 2 78 30 3 48 30 4 18 18 5 0 0 1 100 28 2 72 19 3 53 25 4 28 27 5 1 1 1 100 26 2 74 17 3 57 20 4 37 21 5 16 16   Table 2: Daily sales and inventory with the new packaging Day Inventory Sales 1 100 32 2 68 31 3 37 35 4 2 2 5 0 0 1 100 34 2 66 30 3 36 24 4 12 12 5 0 0 1 100 22 2 78 32 3 46 32 4 14 14 5 0 0 [End Selection] Question: Estimate the average rate of sales with the original packaging [orig] Question: Estimate the average rate of sale with the new packaging [new]  

Farmer’s Fridge operates a network of smart vending machines, designed to make finding fresh meals as simple as buying a candy bar from a vending machine.  The company now has over 2,000 fridges in airports, office building, hospitals and universities across the country.  The company is considering how best to stock its Steakhouse Chopped Salad at its fridge at the Metropolitan Museum of Art in Central Park, NYC.  Steakhouse Chopped Salads typically last 6 days in the fridge and are restocked every 5 days. Any unsold salads are composted and the containers recycled.  A Steakhouse Chopped Salad costs approximately $5 and sells for $15.  The company is testing a new AI powered forecasting system. Table 1 shows sales and forecasted sales of Steakhouse Chopped Salad at the Metropolitan Museum of Art fridge over the past ten 5-day replenishment cycles. That data is the result of a 50-day experiment in which the fridge was completely stocked with 110 Steakhouse Chopped Salads and nothing else. Over the coming weeks, the company plans to use the results of the experiment to manage how it stocks the fridge with Steakhouse Chopped Salads, Apple Pecan Salads, etc.    [Start Selection] Table 1. Performance of AI forecasting system for Steakhouse Chopped Salad at the Metropolitan Museum of Art fridge over the past ten 5-day replenishment cycles 5-day Period Sales Forecast 1 51 49 2 111 70 3 40 70 4 83 49 5 13 27 6 15 15 7 14 10 8 7 11 9 9 15 10 40 27 [End Selection] The AI system forecasts demand for 50 Steakhouse Chopped Salads at the Metropolitan Museum over the coming 5-day period.  Assuming the appropriate Normal Distribution, answer the following questions: Question: Given the forecast for 50 Steakhouse Chopped Salads, how many of those salads should Farmer’s Fridge stock the fridge with for the next 5-day period in order to maximize its expected profits. [MaxExpProfit]  Question: What are Farmer’s Fridge’s maximum expected profits from Steakhouse Chopped Salads at the Metropolitan Museum over the coming 5-day period? [MaxProfits] Question: To achieve these expected profits, how many Steakhouse Chopped Salads must Farmer’s Fridge expect to compost from the fridge at the Metropolitan Museum at the end of the coming 5-day period? [compost] Question: Farmer’s Fridge is concerned about its environmental impact and wishes to ensure it composts at most 20% of the salads it stocks. If the company wants to expect to meet this standard, how many Steakhouse Chopped Salads should Farmer’s Fridge stock the fridge with for the next 5-day period? [wastelimit] Question: How much less profit should Farmer’s Fridge expect to earn from Steakhouse Chopped Salads over the next 5-day period if it limits the fraction of salads composted to 20%? [lost]

Farmer’s Fridge operates a network of smart vending machines, designed to make finding fresh meals as simple as buying a candy bar from a vending machine.  The company now has over 2,000 fridges in airports, office building, hospitals and universities across the country.  The company is considering how best to stock its Steakhouse Chopped Salad at its fridge at the Metropolitan Museum of Art in Central Park, NYC.  Steakhouse Chopped Salads typically last 6 days in the fridge and are restocked every 5 days. Any unsold salads are composted and the containers recycled.  A Steakhouse Chopped Salad costs approximately $5 and sells for $15.  The company is testing a new AI powered forecasting system. Table 1 shows sales and forecasted sales of Steakhouse Chopped Salad at the Metropolitan Museum of Art fridge over the past ten 5-day replenishment cycles. That data is the result of a 50-day experiment in which the fridge was completely stocked with 110 Steakhouse Chopped Salads and nothing else. Over the coming weeks, the company plans to use the results of the experiment to manage how it stocks the fridge with Steakhouse Chopped Salads, Apple Pecan Salads, etc.    [Start Selection] Table 1. Performance of AI forecasting system for Steakhouse Chopped Salad at the Metropolitan Museum of Art fridge over the past ten 5-day replenishment cycles 5-day Period Sales Forecast 1 107 49 2 68 70 3 31 70 4 31 49 5 20 27 6 18 15 7 15 10 8 7 11 9 12 15 10 17 27 [End Selection] The AI system forecasts demand for 50 Steakhouse Chopped Salads at the Metropolitan Museum over the coming 5-day period.  Assuming the appropriate Normal Distribution, answer the following questions: Question: Given the forecast for 50 Steakhouse Chopped Salads, how many of those salads should Farmer’s Fridge stock the fridge with for the next 5-day period in order to maximize its expected profits. [MaxExpProfit]  Question: What are Farmer’s Fridge’s maximum expected profits from Steakhouse Chopped Salads at the Metropolitan Museum over the coming 5-day period? [MaxProfits] Question: To achieve these expected profits, how many Steakhouse Chopped Salads must Farmer’s Fridge expect to compost from the fridge at the Metropolitan Museum at the end of the coming 5-day period? [compost] Question: Farmer’s Fridge is concerned about its environmental impact and wishes to ensure it composts at most 20% of the salads it stocks. If the company wants to expect to meet this standard, how many Steakhouse Chopped Salads should Farmer’s Fridge stock the fridge with for the next 5-day period? [wastelimit] Question: How much less profit should Farmer’s Fridge expect to earn from Steakhouse Chopped Salads over the next 5-day period if it limits the fraction of salads composted to 20%? [lost]

Farmer’s Fridge is concerned with stocking the fridge at the Metropolitan Museum. Table 1. gives prices, costs, expected demands and standard deviation in demands for the three types of salads.  [Start Selection] Table 1. Price, cost, expected demand and standard deviation in demand for each product Product Price Cost Mean Std Dev Steakhouse Chopped Salad $15.00 $5.00 50 25 Apple Pecan Salad $10.00 $3.00 60 30 Greek Salad $12.00 $4.00 40 20 [End Selection] Assume Normal Distributions. The fridge at the Metropolitan Museum holds at most 150 salads.  Question: How should the company stock the fridge to maximize its expected profits? Ignore integrality.  Number of Steakhouse Chopped Salads to stock: [steakhouse] Number of Apple Pecan Salad to stock: [applepecan] Number of Greek Salads to stock: [greek] Question: What are the company’s maximum expected Revenues? [revenues] Question: What fraction (%) of the products the company stocks should the company expect to compost? [compost]