12:45 # GH MX 5GE will MY NOTES ASK YOUR TEACHER A clothing manufacturer has factories in Atlanta, Chicago, and New York. Sales (in thousands) during the first quarter are summarized in the matrix below. Atl. Chi. N.Y. Coats 43 60 16 Shirts 81 52 44 Pants 19 Ties 10 During this period the selling price of a coat was $200, of a shirt $30, of a pair of pants $60, and of a tie $25. Use matrix multiplication to find the total revenue received by each factory. Atlanta $ 11720 X Chicago $ 14950 New York $ 5235 X : 9. [-/1 Points] DETAILS HARMATHAP11 3.2.046. MY NOTES ASK YOUR TEACHER Matrix A below gives the fraction of the earth's area and the projected fraction of its population for five continents in 2050. Matrix B gives the earth's area (in square miles) and its projected 2050 population.t Fraction Fraction of of Area Population 0.162 0.047 North America 0.119 0.086 South America A= 0.066 0.065 Europe 0.298 0.582 Asia 0.202 0.215 Africa Area Population 57,850,000 Area 0 9,322,000,000 Population Find the area (in square miles) and population of each given continent by finding AB. 10. [-/1.42 Points] DETAILS HARMATHAP11 3.2.047.MI. MY NOTES ASK YOUR TEACHER Suppose that, for a certain metropolitan area and the surrounding counties, during each 5-year period an average of 20% of the metropolitan population M moves to the surrounding counties and the rest remains. Similarly, suppose that in the same period, an average of 30% of the surrounding counties' population S moves to the metropolitan area and the rest remains. This population dynamic can be represented by the following matrix MS [80% 20% ] M _ [0.8 0.2] 30% 70%] S [0.3 0.7] where row 1 shows how the metropolitan population M changed (80% remained in M and 20% moved to S), and row 2 shows how the population of the surrounding counties changed. Currently the population is evenly divided between the two areas, which can be represented by the row matrix P= % in M % ins = [50% 50%] = [0.5 0.5]. (a) Form the product PD. Interpret its entries. After 5 years, M has % and S has % of the population. (b) Predictions of this population distribution after 10 years and after 15 years could be found from what matrix products? 10 years P 15 years P (c) Suppose that at some future time, the populations reach the point where 60% live in the metropolitan area and 40% live in the surrounding counties. Find the predicted distribution 5 years later. M = % S = III O <