A chauffer must decide between driving his clients in the rolls royce or the mercedes benz. the rolls royce costs 1.75 per mile to operate and the mercedes benz costs 2.00 per mile. The chauffer can charge 4.00 per mile for the rolls royce and 6.50 per mile for mercedes benz. The chauffer wants his expenses to be no more than 200 for the day and his total charges to be at least 600 for the day. the rolls royce must travel at most 90 miles and the mercedes benz must travel at least 30 miles
To solve this problem, we need to find out how many miles the chauffeur should drive each car and calculate the expenses and charges for each option.
Let's start with the Rolls Royce:
Let's assume the chauffeur drives x miles using Rolls Royce, where x is a positive number less than or equal to 90.
Expenses for the Rolls Royce = 1.75 * x
Charges for the Rolls Royce = 4.00 * x
Next, let's consider the Mercedes Benz:
Let's assume the chauffeur drives y miles using Mercedes Benz, where y is a positive number greater than or equal to 30.
Expenses for the Mercedes Benz = 2.00 * y
Charges for the Mercedes Benz = 6.50 * y
Now, let's set up the constraints based on the given conditions:
1. The expenses should be no more than $200 for the day:
1.75 * x + 2.00 * y ≤ 200
2. The total charges should be at least $600 for the day:
4.00 * x + 6.50 * y ≥ 600
3. The Rolls Royce must travel at most 90 miles:
x ≤ 90
4. The Mercedes Benz must travel at least 30 miles:
y ≥ 30
Now, we can solve this system of inequalities to find the optimal solution for the chauffeur.
By graphing these inequalities or using a linear programming method, we can find the values of x and y that satisfy all the conditions. The feasible region will be a bounded area, and any point within that area will be a valid solution.
Note: The exact answer may vary based on the specific method used for solving the inequalities.