Question

Zoo Design

Problem Description
Aman is a rich businessman who want to build a zoo. He wants to make enclosures for terrestrial and aquatic animals. Terrestrial animals will be of two types, namely herbivorous and carnivorous animals. So there will be three different enclosures.

Herbivores like Elephant, Deer are prime attractions. Similarly, Lion and Tiger are prime attractions amongst carnivores. Finally, Dolphins and Shark are prime attractions amongst aquatics for tourists.

Aman being a savvy businessman realizes that in order to minimize the cost of building the zoo without compromising on the attractions, he has to decide how much area to allocate to each animal type. Each animal type requires a certain area to thrive in. This in turn impacts the area allocation, which in turn has cost implications.

Your task is to help Aman workout the mathematics such that the zoo building cost is minimized subject to the following constraints:

Zoo needs to have minimum of X herbivores, Y carnivores and Z aquatic animals

Different types of animals will need different minimum area to thrive in

For animals of a given type, the minimum area required is the same

There is also a maximum limit for the overall area allocated for each animal type

Cost of fencing etc. is included in cost of enclosure

Exclude the essentials like pathways for tourists, from area and cost calculations

Consider all areas in square meters and cost in Rupees.

Constraints
0 < number of animals of each type <= 20

0 < max area for each animal type <= 500

0 < total area of land on which zoo is to be built <= 1000

0 < min area required by individual animals <= 15

0 < price of each type of enclosure <= 10000

Area of each type of enclosure should be rounded off to the nearest integer

Input
First line contains three space separated integers denoting the cost per square meter of building the enclosure for each type of animals viz. herbivorous, carnivorous and aquatic respectively

Second line contains three space separated integers denoting the maximum area that can be allocated to each type of animal viz. herbivorous, carnivorous and aquatic respectively

Next three lines, each will contain two space separated integers M and N, for each type of animal viz. herbivorous, carnivorous and aquatic respectively, where M denotes minimum number of animals of that type and N denotes minimum area required for that animal type

Last line contains an integer which represents the total area of land on which the zoo needs to be built

Output
Single integer containing the minimum cost required to build the zoo

Time Limit
1

Answer 1

Answer:

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