ok first we calculate the length of board without losses:
4 * 11.5 = 46 inches
then, we have 1 inch of waste allowed fir each piece, so the total waste is 4*1 = 4 inches
finally, we will add the length of the waste to the desired length to get the total length of the board as follows:
total length of board = 46+4 = 50 inches
