Kate is interested in leasing a new car. She contacts three car dealers and each dealer offered hera closed-end three year (36 months) lease. Additionally, she will not have to put a deposit downat the time of signing. A monthly charge and a mileage allowance is included in each lease. Thereis a per kilometre cost for each additional kilometre over the mileage allowance. For each lease,the monthly cost, mileage allowance and cost per additional kilometre is given in the below table.Lease OptionMonthlyCost (€)Mileage Allowance(km)Cost per AdditionalKilometre (€)Southside Motors 300 30,000 0.20Luxury Motors 325 40,000 0.25Cross Motors 350 55,000 0.20Kate decided to select the lease option that will minimise her total three-year cost. She is unsurehow many kilometres she will drive over the next three years. However, to make this decision,Kate considers it reasonable to assume that she will drive 10,000 km per year, 15,000 km peryear or 20,000 km per year.

To determine which lease option will minimize Kate's total three-year cost, we need to calculate the total cost for each lease option under the three different driving scenarios (10,000 km/year, 15,000 km/year, 20,000 km/year).

1. Southside Motors:

   • Monthly cost for 3 years: 300€ * 12 months * 3 years = 10,800€
   • Cost for additional km:
     • For 10,000 km/year: No additional cost as it's within the mileage allowance.
     • For 15,000 km/year: (15,000 km/year * 3 years - 30,000 km) * 0.20€ = 9,000€
     • For 20,000 km/year: (20,000 km/year * 3 years - 30,000 km) * 0.20€ = 18,000€

2. Luxury Motors:

   • Monthly cost for 3 years: 325€ * 12 months * 3 years = 11,700€
   • Cost for additional km:
     • For 10,000 km/year: No additional cost as it's within the mileage allowance.
     • For 15,000 km/year: No additional cost as it's within the mileage allowance.
     • For 20,000 km/year: (20,000 km/year * 3 years - 40,000 km) * 0.25€ = 10,000€

3. Cross Motors:

   • Monthly cost for 3 years: 350€ * 12 months * 3 years = 12,600€
   • Cost for additional km:
     • For 10,000 km/year: No additional cost as it's within the mileage allowance.
     • For 15,000 km/year: No additional cost as it's within the mileage allowance.
     • For 20,000 km/year: No additional cost as it's within the mileage allowance.

Now, we can compare the total costs for each lease option under the three different driving scenarios:

• For 10,000 km/year: Southside Motors (10,800€) is the cheapest option.
• For 15,000 km/year: Luxury Motors (11,700€) is the cheapest option.
• For 20,000 km/year: Luxury Motors (21,700€) is the cheapest option.

So, depending on how much Kate plans to drive, she should choose either Southside Motors or Luxury Motors.