Question

Problem 2 You are the owner of a car racing team competing in the Formula 1 championship. The cars of your team require two different types of tires: (1) wet tires, which are suitable for driving under heavy rain conditions and (2) dry tires, which work better in sunny days. The number of tires needed by your team for each of the seven races of the championship are listed in Table 3 Type/Race 234567 Wet tires 30 20 40 55 80 150 180 Dry tires 35 2830|50 90150|200 Table 3: Demand of tires per race To satisfy the demand of tires required for each race you have two choices. One possibility is buying race and save the excess for subsequent races. You can also buy fewer tires that the ones you need, as long as you have enough tires in your inventory to fulfill the requirements. For instance, before race 1 you can buy 90 wet tires, which can be used in races 1, 2 and 3. Then, buy 65 tires before race 4, use 55 of those and save the residual 10 for race 5. Subsequently, buy the remaining 70 before that race, and finally buy 150 and 180 before races 6 and 7, respectively. The second option is recycling used tires. After each race, it is possible to recycle all, some, or none of the used tires that you currently have. The tires that are recycled are shipped to a recycling facility that adds rubber and reshapes them until they are as good as new. The recycling process is not immediate, though. If you decide to recycle used tires after a race, it will take the recycling company two races to send those back. For example, if you send 20 of the 30 tires used in race 1, those can only be used from race 3 and onwards. Notice that the combination of buying and recycling tires gives you many interesting options. For example, you can buy 30 wet tires the for the first race and send those to recycle after the race. Then, buy 30 tires before race 2, use 20 and save the remaining 10, which along with the recycled tires from race 1 will cover the demand of race 3. Suppose that the initial inventory of tires is zero.

Answer 1

Considering the Price of the new tyres and the recycled tires, Optimal usage of recycled have been taken wherever necessary,

conditions:

1. If the New Tyre cost is lower than the recycled, then the new tyres are bought

2. Price paid for recycled tyres is as per the buying Race type (eg-1,2,3,4,5,6,7)

3. There can be several permutations of the problem, however the best optimal opeerations managemnet is explained herein as under.

4. The price for the recycled are taken on the race day and not on the sent day-Important point (as the same is not specified in the question)

5. For Race 1 & 2 (only new tyres are procured assuming there is no existing inventory)

6. 3rd Week

a) For 3rd week (WET tyres) - 10 New tyres & 30 old tyres are considered

b) For 3rd week (DRY Tyres) - All 30 old tyres, at third race rate are considerd and 5 are left as inventory

7. 4th Week

a) WET Tyres- All new tyres are considered as the price is lesser than the recycled ones

b) DRY Tyres - 17 new tyres5 from week 3 and 28 from week 2 at th price of current week delivery.

8. 5th Week

a) WET Tyres - All new as the price is lower

b) DRY Tyres - 30 tyres bought at current week price & 60 tyres bought at new tyres rate.

9. 6th Week

a) WET Tyres- All bought new as the new tyres price is lower than the recycled tyres

b) DRY Tyres - 50 from week 4 has been recycled and bought at current week price, remaining 100 are bought as new Tyres

10. 7th Week

a) WET Tyres - 100 new tyres at current price are bought, 80 at recycled price sent for recycling in week 5

b) DRY Tyres -

Race/Type	1	2	3	4	5	6	7
WET Tyres (Total Price)	1764	902	1258	1617	3320	8865	9806
DRY Tyres	1067.5	1615.6	1602	2347.3	2032	3785	8682
Total Race wise	2831.5	2517.6	2860	3964.3	5352	12650	18488

This is an idle solution. We also have several other permutations of buying new and recycled tyres.

Rates have been considered at current delivery race day, as the same is not specified in the question. and the payment for any recycle is made on the delivery date (Week used).