Task 1: Decide how many it costs to make your 2 items. You can't use my numbers, but I will give you an example. Say I am selling slippers and gloves. It costs me $1 to make the slippers and $2 to make the gloves and my investment is 100. I want to graph the possibilities for my job venture based on the cost and my investment that I can't go over. The equation will have the cost of 1st * x + cost of 2nd * x is no greater than $100. The graph should look like this--yours will have numbers on the axes. Choose 1 point in the shaded region, one on the line, and one outside of the shaded region and tell what they mean. For example if (1,4) is in the shaded region it would be 1 represents the number of slippers and 4 represents the number of gloves and I have enough in my budget to make them.

Question

Task 1: Decide how many it costs to make your 2 items. You can't use my numbers, but I will give you an example. Say I am selling slippers and gloves. It costs me $1 to make the slippers and $2 to make the gloves and my investment is 100. I want to graph the possibilities for my job venture based on the cost and my investment that I can't go over. The equation will have the cost of 1st * x + cost of 2nd * x is no greater than $100. The graph should look like this--yours will have numbers on the axes. Choose 1 point in the shaded region, one on the line, and one outside of the shaded region and tell what they mean. For example if (1,4) is in the shaded region it would be 1 represents the number of slippers and 4 represents the number of gloves and I have enough in my budget to make them.

Answer 1

Let's assume that the cost of making the first item is $x and the cost of making the second item is $y. We are given that the investment is $100.

The inequality equation representing the cost and investment constraint can be written as:

x + y ≤ 100

To graph this inequality, we can plot the points on a coordinate plane. Let's label the x-axis as the number of slippers produced (item 1) and the y-axis as the number of gloves produced (item 2).

Here is an example graph:

(x-axis) Number of Slippers (item 1)
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| Shaded Region (below the line)
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|// Line: x + y = 100
(y-axis) Number of Gloves (item 2)

Now, let's choose the following points:

1) Point in the shaded region: (10, 20)
This means producing 10 slippers (x-coordinate) and 20 gloves (y-coordinate). It satisfies the cost and investment constraint, as the combined cost (10*$1 + 20*$2 = $10 + $40 = $50) is less than the investment of $100.

2) Point on the line: (50, 50)
This point lies on the line x + y = 100. It represents producing 50 slippers and 50 gloves. The combined cost (50*$1 + 50*$2 = $50 + $100 = $150) exceeds the investment of $100, so it is on the boundary of what is feasible.

3) Point outside the shaded region: (30, 40)
This point is outside the shaded region, meaning the cost of producing 30 slippers and 40 gloves exceeds the investment of $100. The combined cost (30*$1 + 40*$2 = $30 + $80 = $110) is greater than the investment.