In make vs buy decision the most important thing to consider is relevent cost. In this problem the relevent cost is the per unit variable cost and avoidable fixed cost.
Per unit variable cost is $11 as mentioned in the problem
Per unit avoidable fixed cost is 150,000 x ((1- 0.4) = 0.6) = 90,000 / 30,000 = $3 (the level of production is 30,000 as mentioned in the problem, ignore the 60,000 theoratical capacity). $90,000 is the avoidable fixed cost if part is purchased from outside
It is mentioned in the question that 40% fixed costs are incurrable no matter what the decision will be, therefore the remaining 60% fixed cost is avoidable if Aril Industries decides to purchase the part 730.
Now to realize a net profit the cost of the part should be less than 11 + 3 = $14 (which is the correct answer)
Hope it is clear for you now.
Best regards,
Maqsood A. Qureshi CMA, CDIF, MBA