Explain the value of the reduced cost $(0\mathrm{.}3)$ for the number of plugs to produce.

b$.$ If the gross margin for rails is decreased to $$1\mathrm{.}05,$ can you predict what the optimal

solution and profit will be$?$

c$.$ Suppose that the gross margin for rivets is increased to $$0\mathrm{.}85.$ Can you predict what the

optimal solution and profit will be$?$

d$.$ If the gross margin for clips is reduced to $$1\mathrm{.}10,$ can you predict what the optimal

solution and profit will be$?$ What if the gross margin is reduced to $$1\mathrm{.}00?$

e$.$ Suppose that an additional $500$ minutes of machine capacity is available. How will the

optimal solution and profit change? What if planned maintenance reduces capacity by

$300$ minutes?