Modeling and sensitivity analysis: 1. A manufacturer produces and sells carpets at $400 each. If 10 or fewer carpets are manufactured per week, each carpet costs $260. The manufacturers regular capacity is 10 carpet per week. The manufacturer can hire additional contract workers to bring up its capacity up to 20 carpets per week, but in this case they need to pay overtime, so the cost of making each extra carpet (beyond the usual capacity of 10) goes up to $310. For example, to make 12 carpets, the cost to the manufacturer will be 10 260 + 2 310 = $3220. i) Assume unlimited demand. Write down the formula to calculate the manufacturer's profit. ii) Suppose the manufacturer is target at $2000 per week. How many carpets should they produce? (Round up your answer.) iii) The price of the carpet fluctuates across time. It can vary from $350 to $450. If the manufacturer fixes their production plan at 10 carpets per week, what would be their profits at different prices? (Consider the price range from $350 to $450 with increments of $10.) iv) Set up a data table to determine how changes in the carpets to produce and price of the carpet affect the profit. (Consider the price range from $350 to $450 with increments of $10; Consider the carpets to produce with increments of 1.)