My daughter has been struggling with this algebra problem and I couldn't help help her. Please help! \"Carlo needs to buy at least eight flowers and has $15 to spend. Roses cost $3 per stem and carnations cost $1 per stem. Make a graph at the right to show all possible combinations of roses and carnations that Carlo could buy.\" How would that be graphed.\r
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document.write( "Please and thank you!
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document.write( "For the graph:\r\n" );
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document.write( "Let x = no. of roses\r\n" );
document.write( "Let y = no. of carnations \r\n" );
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document.write( " x + y > 8 (Guarantees there are at least 8 flowers)\r\n" );
document.write( "3x + y < 15 (Guarantees that the total cost does not exceed $15)\r\n" );
document.write( " x > 0 (Guarantees there cannot be a negative number of roses)\r\n" );
document.write( " y > 0 (Guarantees there cannot be a negative number of carnations)\r\n" );
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document.write( "Form the equations of the boundary lines by replacing the \r\n" );
document.write( "inequality symbols by = signs.\r\n" );
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document.write( "These equations are:\r\n" );
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document.write( " x + y = 8 This line has intercepts (0,8) and (8,0)\r\n" );
document.write( "3x + y = 15 This line has intercepts (0,15) and (5,0)\r\n" );
document.write( " x = 0\r\n" );
document.write( " y = 0\r\n" );
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document.write( "The last two equations are just the equations of the\r\n" );
document.write( "y and x axes respectively. They just mean that \r\n" );
document.write( "everything must be in the first (upper right) quadrant,\r\n" );
document.write( "i.e., no negative velues for x or y\r\n" );
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document.write( "Graph the first line using the intercepts:\r\n" );
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document.write( "All points (x,y) ON or ABOVE that line represent\r\n" );
document.write( "combinations of x roses and y combinations which\r\n" );
document.write( "consist of 8 or mor roses. However many of those\r\n" );
document.write( "points, in fact most of them, represent combinations\r\n" );
document.write( "that would cost more than $15.\r\n" );
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document.write( "Now if we draw only the second line, using the intercepts: \r\n" );
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document.write( "Now all points (x,y) ON or BELOW that line represent\r\n" );
document.write( "combinations of flowers whose costs do not exceed\r\n" );
document.write( "$15.\r\n" );
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document.write( "So now we put both lines on the same graph:\r\n" );
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document.write( "Only those points (x,y) in the triangle marked XXX are\r\n" );
document.write( "the possible combinations that he may buy with no more \r\n" );
document.write( "than $15 yet have at least 8 flowers.\r\n" );
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document.write( "Or, erasing the unused portions, we have only this \r\n" );
document.write( "triangle (it is called the \"feasible region\")\r\n" );
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document.write( "The only problem here is that we can't have fractions of flowers, \r\n" );
document.write( "and most of the points in that region involve fractions, so we\r\n" );
document.write( "must grid off the feasible region like this:\r\n" );
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document.write( "and the only possibilities are the points which are corners\r\n" );
document.write( "of the squares, i.e., both of whose coordinates are integers.\r\n" );
document.write( "These are called \"lattice points\". You can count the corners\r\n" );
document.write( "of squares included in or on the triangle. There are 20 of them: \r\n" );
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document.write( "1. (0,8) He could buy 0 roses, 8 carnations, 8 flowers for $8.\r\n" );
document.write( "2. (0,9) He could buy 0 roses, 9 carnations, 9 flowers for $9.\r\n" );
document.write( "3. (0,10) He could buy 0 roses, 10 carnations, 10 flowers for $10.\r\n" );
document.write( "4. (0,11) He could buy 0 roses, 11 carnations, 11 flowers for $11.\r\n" );
document.write( "5. (0,12) He could buy 0 roses, 12 carnations, 12 flowers for $12.\r\n" );
document.write( "6. (0,13) He could buy 0 roses, 13 carnations, 13 flowers for $13.\r\n" );
document.write( "7. (0,14) He could buy 0 roses, 14 carnations, 14 flowers for $14.\r\n" );
document.write( "8. (0,15) He could buy 0 roses, 15 carnations, 15 flowers for $15.\r\n" );
document.write( "9. (1,7) He could buy 1 rose and 7 carnations, 8 flowers for $10.\r\n" );
document.write( "10. (1,8) He could buy 1 rose and 8 carnations, 9 flowers for $11.\r\n" );
document.write( "11. (1,9) He could buy 1 rose and 9 carnations, 10 flowers for $12.\r\n" );
document.write( "12. (1,10) He could buy 1 rose and 10 carnations, 11 flowers for $13.\r\n" );
document.write( "13. (1,11) He could buy 1 rose and 11 carnations, 12 flowers for $14.\r\n" );
document.write( "14. (1,12) He could buy 1 rose and 12 carnations, 13 flowers for $15.\r\n" );
document.write( "15. (2,6) He could buy 2 roses and 6 carnations, 8 flowers for $12.\r\n" );
document.write( "16. (2,7) He could buy 2 roses and 7 carnations, 9 flowers for $13.\r\n" );
document.write( "17. (2,8) He could buy 2 roses and 8 carnations, 10 flowers for $14.\r\n" );
document.write( "18. (2,9) He could buy 2 roses and 9 carnations, 11 flowers for $15.\r\n" );
document.write( "19. (3,5) He could buy 3 roses and 5 carnations, 8 flowers for $14.\r\n" );
document.write( "20. (3,6) He could buy 3 roses and 6 carnations, 9 flowers for $15.\r\n" );
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document.write( "Edwin
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