1. In the late 1900s, the relationship between the domestic market shares of three major U.S. manufacturers of cars and light trucks could be modeled by x3 = 0.66 2.2x1 0.02x2 where x1, x2, and x3 are, respectively, the fractions of the market held by Chrysler, Ford, and General Motors. Thinking of General Motors' market share as a function of the shares of the other two manufacturers, describe the graph of the resulting function. (Round your answers to the two decimal places.) The graph is a plane with x1 intercept = , x2 intercept = , and x3 intercept = . How are the different slices by x1 = constant related to one another? The slices by x1 = constant are concentric ellipses. The slices by x1 = constant are straight lines which are not lying in the same plane and aren't parallel to each other. The slices by x1 = constant are planes that are parallel to each other. The slices by x1 = constant are straight lines which are lying in the same plane and intersect. The slices by x1 = constant are straight lines that are parallel to each other. What does this say about market share? General Motors' share by percentage points per 1 percentage- point increase in Ford's market share, and this change Chrysler's share. 2. In the late 1900s, the relationship among the domestic market shares of three major manufacturers of breakfast cereal was x1 = 0.4 + 1.2x2 + 2x3 where x1, x2, and x3 are, respectively, the fractions of the market held by Kellogg, General Mills, and General Foods. Thinking of Kellogg's market share as a function of shares of the other two manufacturers, describe the graph of the resulting function. (Round your answers to one decimal place.) The graph is a plane with x1 intercept = , x2 intercept = , and x3 intercept = . How are the different slices by x2 = constant related to one another? The slices by x2 = constant are straight lines that are parallel to each other. The slices by x2 = constant are straight lines which are lying in the same plane and intersect. The slices by x2 = constant are concentric ellipses. The slices by x2 = constant are planes that are parallel to each other. The slices by x2 = constant are straight lines which are not lying in the same plane and aren't parallel to each other. What does this say about market share? Kellogg's share by percentage points per 1 percentage-point increase in General Foods' market share, and this change General Mills' share. 3. The cost C (in dollars) of building a house is related to the number k of carpenters used and the number e of electricians used by C(k, e) = 15,000 + 50k2 + 60e2. If k = e = 16, compare the effects of increasing k by one unit and of increasing e by one unit. The effect of increasing k by one unit is to increase C by $ The effect of increasing e by one unit is to increase C by $ Interpret the result. This means that, if you are currently using to build a house, it would cost you than to hire an additional electrician ($ carpenters and electricians to hire an additional carpenter ($ ) ). 4. Your Cabaret nightspot "Jazz on Jupiter" has become an expensive proposition: You are paying monthly costs of $60,000 just to keep the place running. On top of that, your regular cabaret artist is charging you $5000 per performance, and your jazz ensemble is charging $1000 per hour. Set up a (monthly) cost function for the scenario. (Let C represent the monthly cost in dollars, x represent the number of performances by the cabaret artist per month and y represent the number of hours of jazz per month.) C(x, y)=