Step 1 :First, we need to find the value of x that makes the price $50. We can do this by setting the price function equal to 50 and solving for x.
Step 2 :\(45 - 5 \ln x = 50\)
Step 3 :Subtract 45 from both sides to isolate the logarithm on one side of the equation.
Step 4 :\(-5 \ln x = 50 - 45\)
Step 5 :\(-5 \ln x = 5\)
Step 6 :Divide both sides by -5 to solve for \(\ln x\).
Step 7 :\(\ln x = -1\)
Step 8 :Raise e to the power of both sides to solve for x.
Step 9 :\(x = e^{-1}\)
Step 10 :\(x \approx 0.368\)
Step 11 :However, since the number of units sold must be a whole number, we round 0.368 to the nearest whole number, which is 0.
Step 12 :So, if the price that consumers are willing to pay is $50, no units will be sold.
Step 13 :\(\boxed{0}\)