Alexis Company currently produces and sells $10,000$ units of calculator per year that has a variable cost of $$5$ and a fixed cost of $$250,000.$ The company currently earns a $$100,000$ annual profit. Assume that Alexis has the opportunity to invest in a new machine that will enable the company to reduce variable costs to $$3$ per unit. The investment would cause fixed costs to increase by $$25,000.$

Should Alexis invest in the new technology?