Test/ Assignment 2 Multiple Choice w/ problems

A local bagel shop produces two products: bagels (B) and croissants (C). Each bagel requires 6 ounces of flour, 1 gram of yeast, and 2 tablespoons of sugar. A croissant requires 3 ounces of flour, 1 gram of yeast, and 4 tablespoons of sugar. The company has 6,600 ounces of flour, 1,400 grams of yeast, and 4,800 tablespoons of sugar available for today's production run. Bagel profits are 20 cents each, and croissant profits are 30 cents each. For the production combination of 600 bagels and 800 croissants, which resource is slack (not fully used)?

flour and sugar These resources are not fully utilized. This uses only 6000 of the 6600 available ounces of flour and 4400 of the available 4800 tablespoons of sugar while using all 1400 available grams of yeast.

Consider the following decision scenario: State of Nature High Low Buy 80 0 Rent 70 30 Lease 30 50 If P(high) is .60, the choice for maximum expected value would be:

rent. If P(high) is 0.60, then P(low) = 1.00 - 0.60 = 0.40. EMVBuy = 0.60($80) + 0.40($0) = $48 (i.e., $48,000). EMVRent = 0.60($70) + 0.40($30) = $54 (i.e., $54,000) EMVLease= 0.60($30) + 0.40($50) = $38 (i.e., $38,000) Therefore, Rent is the decision alternative with the maximum EMV.

Consider the following decision scenario: State of Nature High Low Buy 80 0 Rent 70 30 Lease 30 50 The minimax regret strategy would be:

rent. The maximum regret for Buy would be $50,000 from a payoff of $0 under the Low state of nature versus the $50,000 for Lease which is the best payoff under the Low state of nature. The maximum regret for Rent is $20,000 under the Low state of nature and the maximum regret for Lease is $50,000 under the High state of nature. The minimum of the maximum regrets is the $20,000 maximum regret for Rent. Therefore, the minimax regret strategy would be to Rent.

Which of the following choices constitutes a simultaneous solution to these equations? 3x+2y=6 6x+3y=12

x = 2, y = 0

For a linear programming problem with the following constraints, which point is in the feasible solution space assuming this is a maximization problem? 14x+6y≤42 x−y≤3

x = 2, y = 1 This point satisfies both of the listed constraints and the nonnegativity constraints.

A decision maker's worst option has an expected value of $1,000, and her best option has an expected value of $3,000. With perfect information, the expected value would be $5,000. The decision maker has discovered a firm that will, for a fee of $1,000, make her position-risk free. How much better off will her firm be if she takes this firm up on its offer?

$1,000 Subtract the fee from the expected value with perfect information. EVPI = expected payoff under certainty - expected payoff under risk = $5,000 - $3,000 = $2,000. Thus, paying $1,000 for perfect information will leave her an expected $2,000 - $1,000 = $1,000 better off than without the perfect information.

One local hospital has just enough space and funds currently available to start either a cancer or heart research lab. If administration decides on the cancer lab, there is a 20 percent chance of getting $100,000 in outside funding from the American Cancer Society next year, and an 80 percent chance of getting nothing. If the cancer research lab is funded the first year, no additional outside funding will be available the second year. However, if it is not funded the first year, then management estimates the chances are 50 percent it will get $100,000 the following year, and 50 percent that it will get nothing again. If, however, the hospital's management decides to go with the heart lab, then there is a 50 percent chance of getting $50,000 in outside funding from the American Heart Association the first year and a 50 percent chance of getting nothing. If the heart lab is funded the first year, management estimates a 40 percent chance of getting another $50,000 and a 60 percent chance of getting nothing additional the second year. If it is not funded the first year, then management estimates a 60 percent chance for getting $50,000 and a 40 percent chance for getting nothing in the follow

$100,000 The total payoff would be the $50,000 in the first year and the $50,000 in the second year.

An analyst, having solved a linear programming problem, determined that he had 10 more units of resource Q than previously believed. Upon modifying his program, he observed that the list of basic variables did not change, but the value of the objective function increased by $30. This means that resource Q's shadow price was:

$3.00. Because the list of basic variables didn't change, the 10 additional units of resource Q were within the range of feasibility. Thus Q's shadow price was $30/10 = $3.00

A local bagel shop produces two products: bagels (B) and croissants (C). Each bagel requires 6 ounces of flour, 1 gram of yeast, and 2 tablespoons of sugar. A croissant requires 3 ounces of flour, 1 gram of yeast, and 4 tablespoons of sugar. The company has 6,600 ounces of flour, 1,400 grams of yeast, and 4,800 tablespoons of sugar available for today's production run. Bagel profits are 20 cents each, and croissant profits are 30 cents each. What are optimal profits for today's production run?

$380 Use the excel method to find the optimal solution is to produce 400 bagels and 1000 croissants.

One local hospital has just enough space and funds currently available to start either a cancer or heart research lab. If administration decides on the cancer lab, there is a 20 percent chance of getting $100,000 in outside funding from the American Cancer Society next year, and an 80 percent chance of getting nothing. If the cancer research lab is funded the first year, no additional outside funding will be available the second year. However, if it is not funded the first year, then management estimates the chances are 50 percent it will get $100,000 the following year, and 50 percent that it will get nothing again. If, however, the hospital's management decides to go with the heart lab, then there is a 50 percent chance of getting $50,000 in outside funding from the American Heart Association the first year and a 50 percent chance of getting nothing. If the heart lab is funded the first year, management estimates a 40 percent chance of getting another $50,000 and a 60 percent chance of getting nothing additional the second year. If it is not funded the first year, then management estimates a 60 percent chance for getting $50,000 and a 40 percent chance for getting nothing in the follow

$60,000 Choose the option with the highest expected value. The optimum decision alternative is the cancer lab with an expected value of $60,000 versus the $50,000 expected if the heart lab were chosen.

Option A has a payoff of $10,000 in environment 1 and $20,000 in environment 2. Option B has a payoff of $5,000 in environment 1 and $27,500 in environment 2. Once the probability of environment 1 exceeds ________, option A becomes the better choice.

.60 A is better when the likelihood of environment 1 becomes relatively more likely. Solve for the probability P1 at which we would be indifferent between Option A and Option B. Setting EMVA = EMVB means P1($10,000) + (1 - P1)($20,000) = P1($5,000) + (1 - P1)($27,500). This implies $20,000 + P1($10,000 - $20,000) = $27,500 + P1($5,000-$27,500) or P1 = ($27,500 - $20,000)/(-$10,000 + $22,500) = 0.60. Therefore, we would prefer Option A if the probability of environment 1 is greater than 0.60.

A local bagel shop produces two products: bagels (B) and croissants (C). Each bagel requires 6 ounces of flour, 1 gram of yeast, and 2 tablespoons of sugar. A croissant requires 3 ounces of flour, 1 gram of yeast, and 4 tablespoons of sugar. The company has 6,600 ounces of flour, 1,400 grams of yeast, and 4,800 tablespoons of sugar available for today's production run. Bagel profits are 20 cents each, and croissant profits are 30 cents each. Which of the following is not a feasible production combination?

0 B and 1,400 C This uses 5,600 tablespoons of sugar when only 4,800 are available.

Consider the following decision scenario: State of Nature High Low Buy 80 0 Rent 70 30 Lease 30 50 The maximax strategy would be:

buy. Buy is the decision alternative with the best best-case scenario with a maximum PV of $80,000.

Consider the following decision scenario: State of Nature High Low Buy 80 0 Rent 70 30 Lease 30 50 The maximin strategy would be:

lease. Lease is the one for the best worst-case scenario with minimum PVs of $50,000 versus $0 with the buy alternative.