Based on the information answer the questions which follow.
A consultant to Department of Commerce. Government of Bianca has suggested 30 products which have high export potential. Dora an entrepreneur and prospective exporter notices that these products can be grouped in three ways- Machine made goods, Handmade goods and Intermediate goods. Among these 30 products some products are both machine made and intermediate goods but not handmade goods. Few products have a combination of handmade and machine made goods but not intermediate goods. Some products are handmade and intermediate goods but not machine made goods. Further it is seen that handmade-machine made goods are I less than machine made-intermediate goods. Similarly the total number of handmade-intermediate goods is I less than machine made-intermediate goods. There are just 4 products common across all product groups i.e. machine made-handmade- intermediate goods. Apart from this the number of only handmade goods is same as only machine made goods but less than only intermediate goods. Each product group/combination has at least one product. Dora prefers to export machine made goods and avoid hand made goods. She finds out that only handmade goods are twice the only machine made-intermediate goods and the number of only intermediate goods is an even number. Whereas her close friend Sara prefers to export intermediate goods followed by only handmade goods.
Sara and Dora prefer to export as many common products as possible in order to understand the regulatory conditions. Keeping their preferences intact, what is the maximum number of common products which can be exported by both of them?
It is given, y = 2x
z > y and z is even
y = 2x
2y + 3x + z + 2 = 30
7x + z = 28
Only x = 2 and z = 14 satisfies the given conditions.
Maximum common products both Dora and Sara can export = Products common to Machines and Intermediates only = x = 2
The answer is option A.
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