(25 points) Hanes has a production technology that can transform cotton (c, measured in pounds) and labor (6, measured in work hours) into either t-shirts (t) or facemasks (f), but not both. Its technology for producing t-shirts is given by t = =ved. To comply with strict government safety standards, Hanes produces facemasks with the production function f = " min{c, (/2}, meaning that producing - facemasks may only be done with 1 pound of cotton and 2 hours of labor. Denote the input prices we and we. (a) Set up the cost minimzation problem for Hanes to produce { t-shirts. Find the conditional factor demand and cost functions. (b) Set up the cost minimzation problem for Hanes to produce f facemasks. Find the conditional factor demand and cost functions. (c) Suppose we = we = $1. The marketing department at Hanes estimates that they can sell 2 million t-shirts for $45 each or 20 million facemasks for $1.5 each. Which good does Hanes choose to produce, and what is their profit? (d) A pandemic strikes, and the demand for facemasks surges. The marketing depart- ment now estimates that they can sell 100 million facemasks for $6 each, with no change to demand for t-shirts. Which good does Hanes choose to produce, and what is their profit? (e) In an effort to prevent profiteering from a crisis, the government requires that Hanes charge $1.5 per mask. If Hanes can still sell up to 100 million masks at this reduced price, which good does Hanes choose to produce? What is the smallest price ceiling such that Hanes would still be willing to produce the 100 million masks instead of t-shirts