seeds of type a and b are sold in packets each containing both type a and b seeds
at last twice the number of twice b seeds as there are in type a seeds and no more than 12 seeds
a) using a scale of 1cm for each unit on both axis draw a graph n the axis to represent the inequalities
b) if the profit of 30 cent is made on the sale of x shirt and 60 cents on type y, determine the packet of seeds on which maximum profit will be made
50
a) To draw the graph to represent the inequalities given in the problem, we will represent the number of type A seeds on the x-axis and the number of type B seeds on the y-axis. Let's go through each inequality step by step:
1. "At least twice the number of type B seeds as there are in type A seeds": This means the number of type B seeds should be greater than or equal to twice the number of type A seeds. We can represent this as y >= 2x.
2. "No more than 12 seeds": This means the total number of seeds should not exceed 12. Since each packet contains both type A and B seeds, we can express this constraint as A + B <= 12.
Now, let's plot these inequalities on the graph:
First, draw a line representing y = 2x. Start from the origin (0,0) and move up 2 units vertically for every 1 unit moved horizontally. This line represents the "at least twice the number of type B seeds as there are in type A seeds" condition.
Next, draw a horizontal line at y = 12. This line represents the "no more than 12 seeds" condition.
Shade the region below the line y = 2x (including the line itself) and below the line y = 12. This shaded region will represent the feasible solutions for the given inequalities.
b) To determine the packet of seeds on which maximum profit will be made, we need to compare the profit made on type A seeds (x) and type B seeds (y). The profit for type A seeds is 30 cents per packet, while the profit for type B seeds is 60 cents per packet.
To find the maximum profit, we need to look for the coordinates of the feasible region that give the highest profit. In other words, we need to find the highest y value within the feasible region.
Locate the point within the feasible region with the highest y-coordinate. The packets of seeds represented by this point will yield the maximum profit.
Note: Keep in mind that we are assuming a linear relationship between the number of packets sold and profit, and that the cost and demand of the seeds are not considered in this analysis.