X2

x1+2x2 +x3  14 x1+2x2+4x3  12 x1 x2 +x3 = 2 x3  3 x1; x2 unrestricted (a) [6 points] Reformulate the problem so it is in standard format. (b) [6 points] Reformulate the problem so it is in canonical format. (c) [3 points] Convert the problem into a maximization problem. 2. [20 points] A lathe is used to reduce the diameter of a steel shaft whose length is 36 inches (in.) from 14 in. to 12 in. The speed x1 (in revolutions per minute), the depth feed x2 (in inches per minute), and the length

sex-linked cross. X2 calculations for section data: ap/ap x +/+ | Phenotype | Observed | Expected | (O-E) | (O-E)2 | (O-E)2/E | wt |

production next month X2 = the number of Beta 5 computers scheduled for production next month Maximize | 1,200X1 | + | 1,800X2 | | | (maximize profit) | Subject to: | 20X1 | + | 25X2 | = | 800 | (full employment, 5 workers x 160 hours) | | X1 | | | ≥ | 10 | (make at least 10 Alpha 4 computers) | | | | X2 | ≥ | 15 | (make at least 15 Beta 5 computers) | | | | X1, X2 | ≥ | 0 | (non-negativity constraints) | Optimal Solution: X1 = 10 X2 = 24 Profit = $55,200

simple regression analysis to large numbers of variables, it is convenient to adopt a notation involving subscripts. It will be assumed that X1, X2, X3, . . . denote the variables under consideration. Accordingly X11, X12, X13, . . . will denote the values assumed by the variable X1, and X21, X22, X23, . . . will denote the values assumed by the variable X2, and so on. With this notation, a sum such as X21 + X22 +‏ X23 ‏+… +‏X2N could be written ∑_(j=1)^N▒X_2j , ∑_j▒X_2j , or simply ∑▒X_2 . When no

each batch X2 = number of product 2 produced in each batch MAX:|150 X1 + 250 X2| Subject to:|2 X1 + 5 X2 £ 200| |3 X1 + 7 X2 £ 175| |X1, X2 ³ 0| How much profit is earned per each unit of product 2 produced? a.|150| b.|175| c.|200| d.|250| __B__ 10. A company uses 4 pounds of resource 1 to make each unit of X1 and 3 pounds of resource 1 to make each unit of X2. There are only 150 pounds of resource 1 available. Which of the following constraints reflects the relationship between X1, X2 and resource

Mr. Hurley has a challenge on his hands, the largest of which is that he asked me to figure this out. Ok now seriously we have to being to analyze the problem. The first thing we want to do is identify the variables. In this case our variables will be the number of acres of corn and the amount of wheat that is planted. We will further define them later. Next we have to identify our objective. In this case we are looking to maximize profits and determine if participation in the government program

1. 7.5/8 The height in metres of a ball dropped from the top of the CN Tower is given by h(t)= -4.9t2+450, where t is time elapsed in seconds. (a) Draw the graph of h with respect to time (b) Find the average velocity for the first 2 seconds after the ball was dropped h(0)=(0,450), h(2)=(2,430.4) = (430.4-450)/(2-0) = -9.8m/s √ (c) Find the average velocity for the following time intervals (1) 1 ≤ t ≤ 4 h(1)=(1,445.1) h(4)=(4,371.6) = (371.6-445.1)/(4-1) = -24.5m/s √ (2) 1 ≤ t ≤ 2 h(1)=(1,445

Adjusting Entries – Examples Let’s work with some examples. We are working with a one year accounting period that ends on 12/31/X2. Let’s use a three step process. Step 1 – Analyze the transaction. Step 2 – Record in the journal. Step 3 – Post to the ledger. Example 1: On 12/31/X2 (before the adjusting process), Supplies, an asset, has a balance of $2,500. Employees take a physical account of the supplies on hand. That physical count reveals that $1,200 of supplies remains. Step 1 ‐‐ The balance

Microeconomics Instructor: Prof. Ryan Oprea Prepared by: Aadil Nakhoda BUDGET CONSTRAINT The budget constraint can be described as the following equation: m = p1 x1 + p2 x2 m = income p1 = price of good x1 p2 = price of good x2 Solving the budget constraint: m p1 m p2 = intersect on the x1 -axis = intersect on the x2 axis p1 p2 Slope of the budget line = - Some key points to remember: The a¤ordable bundle of goods lie on or below the budget line, while the una¤ordable bundle of goods

, Case #1: the turbine generator industry The default prediction that we’d make using economic theory (or common sense) in the absence of game theory is that, in the turbine generator case, General Electric should have undercut Westinghouse because the former has lower costs. But we start to see why it didn 't when we introduce capacity constraints into the Bertrand model. Capacity constraints can stem from two things: decreasing returns to scale, or demand-uncertainties that create expected