portfolio management - doubt in eoc

need help in question 9 from eoc. (reading 48) in pm. multifactor models.

question asks how to exploit arbitrage . the factor sensitives and expected returns of three funds are given. My doubt is in the solution they have assumed weights for funds. How do we do this? thanks in advance.

fund exp ret sensitivity

a .02 .5

b .04 1.5

c .03 .9