Consider the total amount you’re willing to spend to start your business. After
selling your items, you want your total amount earned to be at least three times
the amount you originally spent.
a. How much money are you hoping to earn from selling your products?
b. Determine the price you want to sell each item for. Note:You may need to
adjust the original prices that you came up with in Task 1.
c. Write an inequality that represents the fact that you want your total earned
to be at least three times the amount that you originally spent. Be sure to
include the price for each item in this inequality.
d. Graph your inequality. Be sure to label your graph and shade the appropriate
side of the line. In the context of the problem, does the shaded area make
sense? If not, make sure to adjust the original values (the investment and
the sale price for both products) so that your shaded area is reasonable.
e. Choose a point that falls in the shaded region for both this inequality and the
inequality you found in Task 1. Explain what the x-coordinate and ycoordinate represent and the significance in terms of both cost and money
earned of this point falling in the shaded regions.
f. What is the ideal number of items you should produce and sell? Why?
a. The amount of money I am hoping to earn from selling my products is three times the amount I originally spent.
b. To determine the price I want to sell each item for, I need to adjust the original prices I came up with in Task 1. Let's assume the original prices for the two items were $10 and $15. To sell each item for three times the original cost, the new prices would be $30 and $45 respectively.
c. The inequality that represents the fact that I want my total earned to be at least three times the amount originally spent is:
Sale Price of Item 1 * Quantity of Item 1 + Sale Price of Item 2 * Quantity of Item 2 ≥ 3 * (Cost of Item 1 * Quantity of Item 1 + Cost of Item 2 * Quantity of Item 2)
Using the adjusted prices, the inequality becomes:
30x + 45y ≥ 3 * (10x + 15y)
d. To graph the inequality, we plot the x-axis representing the quantity of Item 1 and the y-axis representing the quantity of Item 2. We draw a line with the equation 30x + 45y = 3 * (10x + 15y), and shade the area above or on the line since we want the total earned to be at least three times the amount originally spent. The shaded area makes sense because any coordinate within that region satisfies the inequality.
e. Let's choose a point in the shaded region, such as (4, 2). In this case, the x-coordinate represents the quantity of Item 1 sold, and the y-coordinate represents the quantity of Item 2 sold. The significance of this point falling in the shaded region is that by selling 4 of Item 1 and 2 of Item 2, I would earn at least three times the amount I originally spent.
f. The ideal number of items I should produce and sell depends on various factors, such as demand, production capabilities, and market conditions. It is important to consider these factors and conduct market research to determine the optimal number of items to produce and sell.