Armstrong Valley Bicycles uses a standard part in the manufacture of several of its bikes. The cost of producing $40,000$ parts is $$138,000,$ which includes fixed costs of $$68,000$ and variable costs of $$70,000.$ The company can buy the part from an outside supplier for $$3\mathrm{.}40$ per unit, and avoid $30\%$ of the fixed costs.

If Armstrong Valley Bicycles makes the part, how much will its operating income be$?$

$$49,600$ greater than if the company bought the part

$$90,400$ less than if the company bought the part

$$45,600$ greater than if the company bought the part

$$47,600$ greater than if the company bought the part