The amount of space required by a particular firm is given below, where x and y are, respectively, the number of units of labor and capital utilized. f(x, y) = 1000 sqrt(6x^2 + y^2)suppose that labor costs $480 per unit and capital costs $40 per unit and that the firm has $6000 to spend. determine the amounts of labor and capital that should be utilized in order to minimize the amount of space required. (hint: to minimize f(x, y) it is enough to minimize the function 6x2 + y2.)

Michelle and julie work at a catering company. they need to bake 264 cookies for a birthday party that starts in a little over an hour and a half. each tube of cookie dough claims to make 36 cookies, but michelle eats about 1/5 of every tube and julie makes cookies that are 1.5 times as large as the recommended cookie size.it takes about 8 minutes to bake a container of cookies, but since julie's cookies are larger, they take 12 minutes to bake. a. how many tubes should each girl plan to bake? how long does each girl use the oven? b. explain your solution process what did you make? c. what assumptions did you make?