A designer apparel company produces a line of sunglasses for its new season. The profit function is modeled by the function R(x) below, where p is the price for each pair of sunglasses. R(p) = - 3p² + 1458p – 19000. a) How much money did this company put in at the start to produce these sunglasses? (In other words, what they spent before selling any sunglasses or making any profits off of them.) b) What is the lowest price the company has to sell each pair of sunglasses for in order to break even (in other words, to not lose money but also not make any money)? Round your answer to the nearest penny. C) At what price should the company sell sunglasses to maximize their revenue? d) How much in total revenue will the company make on these sunglasses at this optimal price? e) Match the following with their corresponding feature on the function's graph ] startup cost | total profit at optimal price | price to maximize profit | lowest price to break even a. y-intercept b. x-value of vertex c. y-value of vertex d. x-intercept

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