MS Share prices shown below at the close of every 10 days.

Assuming an investor owns 10,000 shares of MS on Day 0. Design an optimal solution to purchase up to 100 option contracts (@ $15x100 per contract) which works for all three paths. (minimum cost & maximum return) Confirm your solution is optimal. (Please show your work.)

Day:0 10 20 30 40 50 60 70 80 90 210 215 220 225 220 225 230 235 240 245 210 210 212 215 205 195 185 175 165 160 Path 1 Path 2 Path 3 210 215 205 195 185 186 187 188 189 190 Day:0 10 20 30 40 50 60 70 80 90 210 215 220 225 220 225 230 235 240 245 210 210 212 215 205 195 185 175 165 160 Path 1 Path 2 Path 3 210 215 205 195 185 186 187 188 189 190