b) Kenya is in the advanced stages of preparing to manufacture COVID-19 vaccines locally. The Ministry of Health has identified a number of facilities all over the country for consideration for the manufacture of one or more of three vaccines; Johnson and Johnson (JJ), AstraZeneca (AZ) and Pfizer (PF). A feasibility study done by the ministry found out the following:
145 have capacity to manufacture JJ and PF
112 have capacity to manufacture JJ and AZ
156 have capacity to manufacture AZ and PF
321 have capacity to manufacture AZ
35 have no capacity to manufacture any of the three vaccines
79 have capacity to manufacture JJ and AZ but not PF
The number that has capacity to manufacture JJ only is equal to those that have capacity to manufacture PF only.
The number that has capacity to manufacture PF only is twice those that have capacity to manufacture AZ only
Required
(i) Present this information on a Venn diagram and hence determine the number of facilities that:
(ii) have capacity to manufacture all three vaccines
(iii) have capacity to manufacture Pfizer vaccine
(iv) have capacity to manufacture at most one vaccine
(v) were considered