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Pierre considers soda (X) and composite good (Y) to be perfect substitutes. His income is m = $200.  Suppose his utility function is 1. If soda cost $2, how much soda does he consume? [Answer1a1] How much money does he leave for everything else? [Answer1a2] 2. If soda cost $1, how much soda does he consume? [Answer1b1] How much money does he leave for everything else? [Answer1b2] 3. if soda cost $0.5, how much soda does he consume? [Answer1c1] How much money does he leave for everything else? [Answer1c2] Instructions: if any bundle on the budget line may be chosen, please type in exactly the following – Chosen bundle can be any point on the budget line

  The production of a handmade clay pot needs two inputs, labor and clay, to produce its output: a pot. Producing a pot always requires the same amount of clay and the same amount of time. Which of the following production functions could appropriately describe the production process, where C represents pounds of clay and L represents hours of labor?  

An individual has the utility function

Suppose there are 3 bundles – A, B, and C. Gregory strictly prefers bundle A to B, strictly prefers bundle B to C, but also strictly prefers bundle C to A. The assumption that is violated by this preference ordering is:

You ARE required to show work for this problem. Consider a triangle ABC like the one below where C = 67°, a = 63 cm, and b = 5 cm. Find the length of side c and the measure of angle B. Round your answers to one decimal place. general triangle.jpg   c = [BLANK-1] cm B = [BLANK-2] degrees

You ARE required to show work for this problem. Verify the identity below by using fundamental identities to transform the left-hand side of the equation into the right-hand side. Clearly show all steps on your own paper, with the problem number clearly labeled. Click “yes” when you have finished writing your solution to this problem.  identity 1.jpg   

You ARE required to show work for this problem. Find ALL (there are infinitely many) solutions (using a unit circle, not your calculator) for the equation below.  trig eqn.jpg   x=? [BLANK-1]

You ARE required to show work for this problem. Find all solutions to the equation below in the interval [0,2π). eqn 2a.jpg  x = ? [BLANK-1]

Note That you don’t have to type your answers in Question 13 & 14 as the blank link is not active. I will be checking your answer in the work submitted as work is required for both of those questions.

You ARE required to show work for this problem. Use long division to divide:  long division A.jpg   The quotient is: [BLANK-1] The remainder is: [BLANK-2] NOTE: You should type your answers in the blanks above as something like x^3 + x^2 + 1. Please clearly label the problem number. You should scan and upload your work after you have completed all of the problems on this exam.