11. Anna and Mary are tailors. They make x blouses and y skirts each week. Anna does all the cutting and Mary does all the sewing. To make a blouse it takes 5 hours of cutting and 4 hours of sewing. To make a skirt it takes 6 hours of cutting and 10 hours of sewing. Neither tailor works for more than 60 hours a week.
(a) For sewing show that 2x + 5y ≤ 30
(b) Write down another inequality in x and y for the cutting.
(c) If they make at least 8 blouses each week, write down another inequality.
(d) Using 1cm to represent 1 unit on each axis, show the information in parts (a), (b) and (c) graphically. Shade only the required region.
(e) If the profit on a blouse is shs. 3,000/= and on a skirt is shs. 10,000/=, calculate the maximum profit that Anna and Mary can make in a week.