Business and Economics: For a business to make a profit it is clear that revenue R must be greater than cost C; in short, a profit will result only if R>C. if a company manufactures records and its cost equation for a week is C = 300 + 1.5x and its revenue equation is R = 2x, where x is the number of records sold in a week, how many records must be sold for the company to realize a profit?
2x>300+1.5x
0.5x>300
X>600
Therefore,more than 600records must be sold in a week to realize profit
To find the number of records that must be sold for the company to realize a profit, we need to determine the point at which the revenue is greater than the cost. In other words, we need to find the value of x for which R > C.
Given that the cost equation for the business is C = 300 + 1.5x, and the revenue equation is R = 2x, we can substitute these equations into the inequality R > C:
2x > 300 + 1.5x
Now, let's solve for x by first subtracting 1.5x from both sides:
0.5x > 300
Next, let's divide both sides of the inequality by 0.5 to isolate x:
x > 300 / 0.5
x > 600
Therefore, the company must sell more than 600 records in a week to realize a profit.