6. Give the slope of each line. Also, state if the lines are parallel (yes or no). Hint: rewrite to slope-intercept form. AB: 2y
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In the table and chart, we have let x represent numbers of Rock CDs and y represent numbers of Rap CDs.
a) The purple dots represent feasible solutions. Their coordinates are listed in the table (for coordinates on the lines) and as a list of points (for points between the lines).
b) The feasible region for total time in hours is shaded blue.
c) The feasible regiion for total cost is shaded red.
d) The overlap of the two regions is shaded purple. The combinations that are feasible are purple dots in that region.
e) The equations used are listed at the left side of the chart. The equations are labeled by color. (≤112 is the cost equation; ≥75 is the hours equation)
ea) The area that is feasible with respect to both constraints is doubly-shaded.
eba) Too much money is spent to the right of the red line.
ebb) Too few hours are used to the left of the blue line.
f) The line for the desired profit is parallel to the "hours" line, but has x-intercept 10 and y-intercept 6. All the points shown except the two on the lower line will give the desired profit.
g) The higher profit line goes through the points (3, 7) and (8, 4). Those two combinations and the points on or near the upper line above y=4 will meet the higher profit requirement.
a) The purple dots represent feasible solutions. Their coordinates are listed in the table (for coordinates on the lines) and as a list of points (for points between the lines).
b) The feasible region for total time in hours is shaded blue.
c) The feasible regiion for total cost is shaded red.
d) The overlap of the two regions is shaded purple. The combinations that are feasible are purple dots in that region.
e) The equations used are listed at the left side of the chart. The equations are labeled by color. (≤112 is the cost equation; ≥75 is the hours equation)
ea) The area that is feasible with respect to both constraints is doubly-shaded.
eba) Too much money is spent to the right of the red line.
ebb) Too few hours are used to the left of the blue line.
f) The line for the desired profit is parallel to the "hours" line, but has x-intercept 10 and y-intercept 6. All the points shown except the two on the lower line will give the desired profit.
g) The higher profit line goes through the points (3, 7) and (8, 4). Those two combinations and the points on or near the upper line above y=4 will meet the higher profit requirement.