I need a thorough explanation to why this is the solution

4. [20 points] Create a strategy that replicates the following payoff using only Call or Put options with different strikes. Payoff 15 10 5 0 25 30 3'5 45 5'5 60 65 70 ST -5 -10 -15 Construct the cashflow table of the strategy to verify its payoff. Solution: Using call options: Cashflow @ T Position ST E [0, 30) ST E [30, 40) ST E [40, 45) ST E [45, 50) ST E 50, 00) long 1 x P(40) 40 - ST 40 - ST 0 0 0 short 1 x P(30) ST - 30 0 0 0 0 short 2 x C(40) 0 0 2(40 - ST) 2(40 - ST) 2(40 - ST) long 4 x C(45) 0 0 0 4(ST 45) 4(ST 45) short 1 x C(50) 0 0 0 0 50 - ST Total +10 40 - ST 80 - 2ST 2ST - 100 ST - 50