JJ'S FACTORY
The new JJ's factory factory makes approximately 2oo black muscle shirts, 300 pink tank tops, 90 blue v-necks, and 150 green t-shirts. Black muscle shirts cost $10 each, pink tank tops cost $7 each, blue v-necks cost $15 each, and the green t-shirts cost $9 each.
a) Approximately how many of each kind of shirt does the factory make in half a year and what is the profit of each?
Black muscle shirts - 1200 = $12000
Pink tank tops - 1800 = $12600
Blue v-necks - 540 = $8100
Green t-shirts - 900 = $8100
WHY? You multiply the purple vector by six since that represents the six months. The numbers in the purple vector represents the different amounts of each shirt made. We then got the the sum which then turned to be the green vector. We then take that vector and multiply it by the other green vector which is the costs of each kind of shirt to get the sum of money made for each kind of shirts in that six months.
b) What kind of shirts would make the most profit in ten years?
Black muscle shirts = $240000
Pink tank tops = $252000 (made the most money)
Blue v-necks = $162000
green t-shirts = $162000
WHY? We use the same resultant vector we got in part a). This is because that resultant gave us approximately how much was made in six months. We get the twenty infront of it by multiplying ten which is the amount of years we're trying to find the profit for by two since we need two sets of six months to make a year. By multiplying theese together you get the amount of each shirt made in ten years.
c) If the approximated amount of shirts increase by 15% every four months, how many shirts would they make in one year?
WHY? Multiplying the matrix with all the original number of shirts by 1.15 tells how many shirts are made in the first 4 months which is the green matrix. Then we multiply the green matrix to find how many shirts the're making in 8 months. We do this three times because we got to find out how many shirts they are making of each kind by the end of the one year. Since there are 12 months in a year we divide 12 by 4 the number of months when the percentage goes up by 15%.
a) Approximately how many of each kind of shirt does the factory make in half a year and what is the profit of each?
Black muscle shirts - 1200 = $12000
Pink tank tops - 1800 = $12600
Blue v-necks - 540 = $8100
Green t-shirts - 900 = $8100
WHY? You multiply the purple vector by six since that represents the six months. The numbers in the purple vector represents the different amounts of each shirt made. We then got the the sum which then turned to be the green vector. We then take that vector and multiply it by the other green vector which is the costs of each kind of shirt to get the sum of money made for each kind of shirts in that six months.
b) What kind of shirts would make the most profit in ten years?
Black muscle shirts = $240000
Pink tank tops = $252000 (made the most money)
Blue v-necks = $162000
green t-shirts = $162000
WHY? We use the same resultant vector we got in part a). This is because that resultant gave us approximately how much was made in six months. We get the twenty infront of it by multiplying ten which is the amount of years we're trying to find the profit for by two since we need two sets of six months to make a year. By multiplying theese together you get the amount of each shirt made in ten years.
c) If the approximated amount of shirts increase by 15% every four months, how many shirts would they make in one year?
WHY? Multiplying the matrix with all the original number of shirts by 1.15 tells how many shirts are made in the first 4 months which is the green matrix. Then we multiply the green matrix to find how many shirts the're making in 8 months. We do this three times because we got to find out how many shirts they are making of each kind by the end of the one year. Since there are 12 months in a year we divide 12 by 4 the number of months when the percentage goes up by 15%.
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