# Managing Engineering and Technology Study Set 1

## Quiz 5 :Decision Making

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A commercial orchard grows, picks, and packs apples and pears. A peck (quarter bushel) of apples takes four minutes to pick and five minutes to pack; a peck of pears takes five minutes to pick and four minutes to pack. Only one picker and one packer are available. How many pecks each of apples and pears should be picked and packed every hour (60 minutes) if the profit is $3.00 per peck for apples and$2.00 per peck for pears? Solve graphically as a linear program and confirm analytically.
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Solve the equations and construct the coordinates for the following as shown below:
…… (1)
…… (2)
Construct the coordinates for the equation (1) and (2) as shown below:
Calculate the coordinates for the equation (1) by assuming the value of p=0 shown as follows:
Calculate the coordinates for the equation (1) by assuming the value of a=0 shown as follows:
Calculate the coordinates for the equation (2) by assuming the value of p=0 shown as follows:
Calculate the coordinates for the equation (2) by assuming the value of a=0 shown as follows:
Therefore, the coordinates for the equation (1) are (15, 0) and (0, 12)
Therefore, the coordinates for the equation (1) are (12, 0) and (0, 15)
The first equation represents the picking constraint. There are a total of 60 minutes of picking available from the single picking in one hour.
The variables a , p represent the number of apples and pears harvested, respectively.
The second equation represents the packing constraint. The graph of these two equations is as follows.
The graph indicates that 6.7 apples and 6.7 pears should be harvested to maximize the use of labor. However, the profit for harvesting these many fruits is $33.5. If only apples are harvested, then 12 apples can be harvested in one hour, which gives a profit of$36.
Thus, optimal profit decision is to harvest only apples.

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You must decide whether to buy new machinery to produce product X or to modify existing machinery. You believe the probability of a prosperous economy next year is 0.6 and of a recession is 0.4. Prepare a decision tree, and use it to recommend the best course of action. The applicable payoff table of profits (+) and losses (-) is:
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Given
In the given problem a company has two options of either to buy new machinery or to modify the existing one in order to produce the product X. There are two probabilities that are associated with the two outcomes. There is a possibility of prosperity (0.6) and that of recession (0.4) that has an impact on the two options.
The table given below gives the two possible options and the payoffs associated with the respective options.
A decision tree based on the data as provided in the table given above can be drawn as given below:
Thus, the expected payoff that is obtained from the option of buying new machinery in order to produce product X is $450,000. On the other hand the expected payoff obtained from the option of modifying the existing machinery is$540,000.
Thus, the decision that should be taken is to modify the existing machinery in order to produce product X as the expected payoff in that case is more than the expected payoff obtained in the case of buying a new machinery.

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You operate a small wooden toy company making two products: alphabet blocks and wooden trucks. Your profit is $30.00 per box of blocks and$40.00 per box of trucks. Producing a box of blocks requires one hour of woodworking and two hours of painting; producing a box of trucks takes three hours of woodworking, but only one hour of painting. You employ three woodworkers and two painters, each working 40 hours a week. How many boxes of blocks ( B ) and trucks ( T ) should you make each week to maximize profit? Solve graphically as a linear program and confirm analytically.
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Linear programming model is used to obtain maximum profits, by utilizing minimum resources available. It helps the decision makers to take effective decisions by using the resources productively. It helps in minimizing cost of operations. It consists of objective function, model constraints and decision variables.
Formulate the LPP to solve this problem graphically, first use the following constraint equations and plot a graph.
The first equation represents the painting constraint. There is a total of 80 hours of painting available from the two painters in one week.
The two variable b and t represent the number of blocks and trucks produced, respectively.
The second equation represents the wood working constraint.
Construct a graph using the following methodology as explained below:
Consider B as x and T as Y for the coordinate calculation.
Calculate coordinates for equation (1) as shown below:
Step: 1 Calculate the coordinates for the equation (1) by assuming the value of y=0 shown as follows:
Calculate the coordinates for the equation (1) by assuming the value of x=0 shown as follows:
Therefore, the coordinates for the equation (1) are (40, 0) and (0,80).
Calculate coordinates for equation (2) as shown below:
Step: 1 Calculate the coordinates for the equation (2) by assuming the value of y=0 shown as follows:
Calculate the coordinates for the equation (2) by assuming the value of x=0 shown as follows:
Therefore, the coordinates for the equation (1) are (120, 0) and (0,40).
Construct a graph by using the above coordinates as shown below:
From the above graph, it can be identified that points O, D and B are in the feasible region. Notice the green region having coordinates of x 1 =24 and x 2 = 32, which satisfies the objective function as follows:
Substitute the values of x 1 and x 2 in the objective function as shown below:
Therefore, from the above graphical analysis it indicates that the optimal number of blocks is 24 , and the optimal number of trucks is 32. Solving the system of equations will give the same result.

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f you have no idea of the economic probabilities pj in Question 5-4, what would be your decision based on uncertainty using ( a ) maximax, ( b ) maximin, ( c ) equally likely, and ( d ) minimax regret assumptions?
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Use a concrete example showing the five-step process by which management science uses a simulation model to solve real-world problems.
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If you have no idea of the economic probabilities pj in Question 5-6, what would be your decision based on uncertainty using ( a ) maximax, ( b ) maximin, ( c ) equally likely, and ( d ) minimax regret assumptions?
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Solve the drilling problem (Table) by using a decision tree. Well Drilling Example-Decision Making Under Risk
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Give some examples of each of the three "occasions for decision" cited by Chester Barnard. Explain in your own words why Barnard thought the third category was most important.
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Describe an example from an organization you know or have read about where a common database is used for a number of different purposes. Also, can you describe an example where a common database is not used for a number of different purposes?
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Your company has proposed to produce a component for an automobile plant, but it will not have a decision from that plant for six months. You estimate the possible future states and their probabilities as follows: Receive full contract (N1, with probability p1 = 0.3); receive partial contract (N2, p2 = 0.2); and lose award (no contract) (N3, p3 = 0.5). Any tooling you use on the contract must be ordered now. If your alternatives and their outcomes (in thousands of dollars) are as shown in the following table, what should be your decision?
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You are considering three investment alternatives for some spare cash: Old Reliable Corporation stock ( A 1), Fly-By-Nite Air Cargo Company stock ( A 2), and a federally insured savings certificate ( A 3). You expect the economy will either "boom" ( N 1) or "bust" ( N 2), and you estimate that a boom is more likely ( p 1 = 0.6) than a bust ( p 2 = 0.4). Outcomes for the three alternatives are expected to be (1) $2,000 in boom or$500 in bust for Old Reliable Corporation; (2) $6,000 in boom, but -$5,000 (loss) in bust for Fly-By-Nite; and (3) \$1,200 for the certificate in either case. Set up a payoff table (decision matrix) for this problem, and show which alternative maximizes expected value.