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MATH 2080 b) determine matrix B, of the cost per student per credit-hour Midterm 4.2: Aplicacion de matrices c) determine the product AB, and Valor: 50pts d) interpret the result. (SET E) 4. Beverages were sold to men, women, and children at a school basketball game in the For each of the following problems, correctly apply matrix algebra concepts to solve each quantities and prices shown in Figures 1 and 2. situation. Correctly use mathematical notation and remember to justify each of the required mathematical processes. Express the solution in the context of the situation. In the event that Figure 1 the result is a decimal, you will round it to two decimal places. Amounts 1. A company produces soft drinks that come in three different flavors: apple, orange, and Coffee Milk Cola strawberry, and two different containers: bottle and can. Below are two tables that Men 250 15 300 summarize the company's total sales between last month and this month. Women 200 35 200 Children 100 500 Bottles Apple Orange Raspberry Last month sodas 130 86 246 Figure 2 Current month sodas 168 90 224 Price Coffee $0.75 Can Apple Orange Raspberry Milk $1.00 Last month sodas 169 86 238 Cola 151 76 $1.50 Current month sodas 212 Write two arrays to represent last month's sales and this month's sales. Then, apply matrix Calculate how much money they spent: algebra concepts to find the average sales of each flavor and package of soda over the 2- a) men month period. (5 points) b) women c) children 2. A health insurance company wishes to establish a prevention program for the community. Among the variables taken into account is the life expectancy of people in rural and urban areas, as presented in the following table: Urban Area Rural Area Year Men Women Men Women 1980 62.1 66.6 51.1 45.2 5. Each of the following four factories produces three products at the daily amounts and 2000 67.4 74.1 61.1 67.4 unit costs given in Figures 1 and 2. Find a suitable parent product to represent the 2004 70.7 78.1 63.8 72.5 production costs 2006 74.9 80.1 68.3 75.2 2008 75.1 80.3 68.7 75.6 Figure 1 2010 75.7 80.8 69.5 76.3 Production Amount Factory Product A Product B Construct a matrix W containing the life expectancy for the urban area and a matrix B for the Product C life expectancy for the rural area. Apply matrix algebra concepts to find the difference San Juan 50 20 25 between urban and rural areas. What can you conclude from this result? Caguas 30 15 24 Mayaguez 20 10 26 Ponce 15 25 22 3. Alicia and Nick attend ABC College and XYC University, respectively. The number of credit-hours taken and the cost per credit this year is presented in the following table. Figure 2 ABC XYZ Cost hour- credit Unit cost of production Alicia 12 6 ABC 100.00 Night Shift Nick 12 Day Shift XYZ 550.00 Product A 2.7 Product B 2.5 4.6 3.8 3.7 Using matrix algebra: Product C a) determine matrix A, which represents the number of credit-hours taken by each student