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 a budget of $400,000 per year to pay employees' salaries.

Write and solve two inequalities that describe the number of employees Donald can hire.

Demand: at least 36 units

6 units per employee
Yearly salary deduction: -$50,000
Maximum budget: -$400,000

Edit:

Maximum budget: $400,000

(NOT negative as I stated above)

Let's define the variables:

- Let E be the number of employees Donald can hire.
- Let S be the yearly salary for each employee.
- Let P be the production per employee per day.
- Let D be the minimum demand per day.
- Let B be the total budget per year.

Based on the given information:
- Each employee produces 6 units per day, so P = 6.
- The minimum demand per day is 36 units, so D >= 36.
- Each employee's yearly salary is $50,000, so S = $50,000.
- The total budget per year is $400,000, so B = $400,000.

To find the number of employees Donald can hire, we need to consider two conditions: the production capacity of employees and the budget constraint.

First, let's consider the production capacity:
The total production per day should be greater than or equal to the minimum daily demand.
The production per employee per day multiplied by the number of employees should be greater than or equal to the minimum daily demand.
P * E >= D
6E >= 36

Next, let's consider the budget constraint:
The total yearly salary for all employees should be less than or equal to the budget.
The yearly salary per employee multiplied by the number of employees should be less than or equal to the budget.
S * E <= B
$50,000E <= $400,000

Now, we have the following two inequalities:
6E >= 36
$50,000E <= $400,000

These inequalities describe the number of employees Donald can hire.

To find the number of employees Donald can hire, we need to set up two inequalities based on the production capacity and the budget constraints.

Let's represent the number of employees as 'x'.

1. Production capacity inequality:
Donald expects to produce 6 units per employee, and the demand is at least 36 units per day. So the production capacity inequality is:
6x ≥ 36

2. Budget inequality:
Donald plans to pay each employee a yearly salary of $50,000, and his budget is $400,000 per year. Hence, the budget inequality is:
50,000x ≤ 400,000

Now, let's solve these inequalities to find the range of acceptable values for 'x'.

1. Production capacity inequality:
6x ≥ 36 Divide both sides by 6 to isolate 'x':
x ≥ 36/6 -> x ≥ 6

2. Budget inequality:
50,000x ≤ 400,000 Divide both sides by 50,000 to isolate 'x':
x ≤ 400,000/50,000 -> x ≤ 8

Therefore, the range of acceptable values for the number of employees 'x' is:
6 ≤ x ≤ 8

So, Donald can hire between 6 and 8 employees for his small business, considering both the production capacity and the budget constraints.