Question

To make a profit, a company’s revenue must be greater than its operating costs. The company’s revenue is modeled by the expression 7.5x – 100, where x represents the number of items sold. The company’s operation costs are modeled by the expression 79.86 + 5.8x. How many items does the company need to sell to make a profit? The inequality that will determine the number of items that need to be sold to make a profit is ? The solution to the inequality is ? The company must sell at least?  items to make a profit.

Answer 1

Revenue = 7.5x - 100
Operation Costs = 5.8x + 79.86

To break even, operation cost = Revenue
⇒ 7.5x - 100 = 5.8x + 79.86
7.5x = 5.8x + 179.86 (Add 100 to both sides)

7.5x - 5.8x = 179.86
1.7x = 179.86
x = 105.8

This implies that the company will need to sell at least 106 items to make a profit.

The inequality that will determine the number of items at need to be sold to make a profit is x ≥ 106

The solution to the inequality is as follows

Revenue = 7.5x - 100
if x =106
Revenue = 7.5(106) - 100
Revenue = 695

Operational Cost = 5.8x + 79.86
if x = 106
Operational Cost = 5.8(106) + 79.86
Operational Cost = 694.66

Profit ≥ (695 - 694.66)
Profit ≥ 0.34

The company must sell at least 106 items to make a profit.

Answer 2

Answer:

1. 7.5x - 100 > 79.86 + 5.8x (Option A)

2. x > 105.8 (Option D)

3. 106 (Option D)

Step-by-step explanation:

Just completed the assignment and got 100%. Hope this helps :)