Alpha Limited is planning to launch a new product in the market. It has undertaken a survey on the product$$s color, brand name and packaging. The company sent $200$ questionnaires to potential customers to obtain their views on the three attributes of the product. The results were as follows:

$24$ persons liked the packaging and the brand name.

$77$ persons liked the brand name or the color but did not like the packaging

$40$ persons liked the color only

$120$ persons liked the color or brand name

$23$ liked the color and packaging

$43$ persons liked at least two of the three attributes

$5$ persons did not like any of the three attributes

$$ The questionnaires of $25$ persons were not received back

The company$$s policy is to incorporate an attribute in the product if at least $50$ percent of the respondents liked the attribute.

Required:

a$.$ Present the above information in a venn diagram. $(5$ marks$)$

b$.$ Number of persons who liked all the three attributes. $(2$ marks$)$

c$.$ Attribute$($s$)$ to be incorporated in the product. $(3$ marks$)$