A department store has 700 pairs of purple Capri stretch pants that it must sell in the next four weeks. The store manager knows that demand by week for the next four weeks will be linear each week, with the following price-response functions: Week 1: d₁(p₁) =1000-100*p₁ Week 2: d₂(p₂) = 800-100*p₂ Week 3: d₃(p₃) = 700-100*p₃ Week 4: d₄(p₄) = 600-100*p₄ Assume that the demands in different weeks are independent, i.e., customers who did not buy in a given week will not come back in subsequent weeks.

Question 1: Assume the store can charge different prices for different weeks. Build an optimization model and an Excel model to identify the optimal weekly prices. Under the optimal prices, the corresponding revenue is $ ???

any computations needed to solve the question are highly appreciated! Id love to figure out how to solve this on my own!