Donald is hiring employees for his new small business. he expects to produce 6 units per employee, and he expects demand to be at least 36 units per day. he plans to pay each employee a yearly salary of $50,000, and has budget of $400,000 per year to pay employees’ salaries.
part a write and solve two inequalities that describe the number of employees donald can hire. graph both solutions on the same number line and use the graph to list three possible numbers of employees that meet the reqirements.
part b after more research, donald expects the demand to be at least 60 units per day instead of 36 units per day. is there any number of employees that meets these new requirements? explain your answer.

i think it is 70

step-by-step explanation:

0.038

step-by-step explanation:

step-by-step explanation:

a) 40 more; b) old factory:   10%, new factory:   16%; c) week 4

explanation:

a) at week 0, we see in the graph that the new factory produces 190 specialty items.  

using the function, substituting 0 in for w,

this is a difference of 230-190 = 40.

b) the function for the old factory is written in the form f(x) = a(1+r)ˣ, where a is the original amount, x is the amount of time and r is the growth rate.   the equation for the old factory is ; 230 is in place of a and is the original amount; w is the amount of time; which means 1+r = 1.1.   this means that r must be 0.1 or 10%.

for the new factory, we find the percent of increase to find the growth rate; the formula for this is

between the first two points, the amount of change is 220-190 = 30; this gives us

30/190 = 0.158 ≈ 0.16 = 16%

c) at week 0, the old factory has 230 while the new factory has 190.

at week 1, the old factory has 230(1.1) = 253 while the new factory has 220.

at week 2, the old factory has 230(1.1²) = 278.3 while the new factory has 252.

at week 3, the old factory has 230(1.1³) = 306.13 while the new factory has 290.

at week 4, the old factory has 230(1.1⁴) = 336.743 while the new factory has 337.   this is the first week that the new factory surpasses the old.