The adventurers learn that the mob boss demands a minimum of 12 watches and 30 rings to be sold every day, and has figured out how to get what he wants while paying his two workers the least possible amount (while still honouring their agreed-upon hourly wages). While Lara and Harrison can't tell how many hours each worker spends selling the jewelry, or how many items they actually sell each day, they did learn something about the workers' wages and how efficiently they both work.
How long do the two workers sell jewelry each day?
How many counterfeit watches and rings do they sell each day?
Without information about the workers' wages and efficiency, it is not possible to determine how long they sell jewelry or how many counterfeit watches and rings they sell each day.
Based on the given information, it is not possible to determine the exact number of hours each worker spends selling jewelry or the exact number of items they sell each day. However, I can provide you with a step-by-step process to calculate the possible combinations based on the given minimum requirements.
Step 1: Define Variables
Let's assume the two workers are named Worker 1 and Worker 2. We'll use the following variables:
- H1: The number of hours Worker 1 spends selling jewelry.
- H2: The number of hours Worker 2 spends selling jewelry.
- W: The number of counterfeit watches sold each day.
- R: The number of counterfeit rings sold each day.
Step 2: Set up Equations
Based on the minimum requirements given:
- Worker 1 sells at least 12 watches and 30 rings per day.
- Worker 2 sells at least 12 watches and 30 rings per day.
We can write the equations as:
1. H1 * W + H1 * R ≥ 12 (equation for Worker 1)
2. H2 * W + H2 * R ≥ 12 (equation for Worker 2)
3. H1 * W + H1 * R ≥ 30 (equation for Worker 1)
4. H2 * W + H2 * R ≥ 30 (equation for Worker 2)
Step 3: Find Possible Combinations
Since we don't have specific information about the exact number of items sold per hour, we can look for multiple combinations that satisfy the minimum requirements.
For example, considering Worker 1 has a high efficiency rate compared to Worker 2:
- Let's assume H1 = 6 and H2 = 1.
- Substituting the values into the equations, we get:
6 * W + 6 * R ≥ 12
1 * W + 1 * R ≥ 12
6 * W + 6 * R ≥ 30
1 * W + 1 * R ≥ 30
Solving these equations will give us a range of possible combinations for W and R.
Step 4: Solve Equations
Solve the equations and inequalities to obtain the possible range of values for W and R. You can use various mathematical techniques such as substitution, elimination, or graphical methods to solve the equations.
Please note that without additional information about the efficiency rates or any constraints on the number of hours worked, it is not possible to determine the exact values of H1, H2, W, and R.
However, by following the steps outlined above, you can explore various possible combinations that satisfy the given minimum requirements.