Your weekly cost (in dollars) to manufacture x cars and y trucks is C(x, y) = 18
ID: 3354416 • Letter: Y
Question
Your weekly cost (in dollars) to manufacture x cars and y trucks is C(x, y) = 180,000 + 6,000x + 3,000% (a) What is the marginal cost of a car? Of a truck? HINT [See Example 1.] marginal cost of a car marginal cost of a truck (b) Describe the graph of the cost function C. HINT [See Example 7.] The graph is a Select-: with x-intercept x = ,y-intercept y- , and z-intercept z = (c) Describe the slice x-10 The slice x = 10 is the straight line with equation z = What cost function does this slice describe? It describes the cost function for the manufacture of Select- if Select-- production is held fixed at 10 cars per week (d) Describe the level curve z = 380,000. The level curve z 380,000 is the straight line What does this curve tell you about costs? It describes the number of cars and trucks you can manufacture to maintain weekly costs at $380,000. It describes the amount of money needed to maintain production of 380,000 cars and trucks per week. It describes cost of producing a certain number of cars if the number of trucks produced each week is fixed at 380. It describes cost of producing one more truck when the number of cars produced each week is fixed at 380 It describes cost of producing a certain number of trucks if the number of cars produced each week is fixed at 380.Explanation / Answer
a) Marginal cost = D/dx( Z)
Marginal cost w.r.t x = 6000
Marginal cost wrt y=3000
b) Graph is a surface with x-intercept=-180000/6000 = -30 , y-intercept = -60 and z-intercept=180000
c) Z = 180000+6000*10+3000y = 240000+3000 y
It describes cost function for manufactur of 1 truck if car production is held constant.
d) Z=380000 = 180000+6000x+3000y
Straght line 6000x+3000y=200000
It describes number of cars and trucks you can manufacture for weekly costs of 380000
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