Consider the following information for an item for which you must develop an inventory policy.  Annual demand:                         4000 units                                  Order cost:                                  $50 per order                            Per unit holding cost / year:      25% of unit purchase price    Per unit purchase cost:              $10.00 if order quantity < 1000 units                                                       $ 9.50 if 1000  5000 units If your supplier decided to stop offering the quantity discounts you see above, and just told you that all items would cost $10 each, your economic order quantity would be

Suppose for the same problem as in the previous question, the profit per unit produced of X and Y was 8 and 4 dollars, respectively.  The appropriate objective function for this would be:

p4.png A way to simulate gravity in space is to shape the space station like a cylindrical shell that rotates, with the astronauts living on the inside surface as shown.  If the radius of the space station is 750 m, at what angular speed would it have to rotate so that the astronauts experience the same normal force standing on the station that they would on Earth?

A satellite of mass 500 kg undergoes a circular orbit of radius 8000 km and a constant speed of 7060 m/s.  What is the acceleration of the satellite?

For the next two questions, suppose you had the following output from LINGO for some linear program.    Variable            Value      Reduced Cost         X1         6.000000          0.400000         X2         0.000000          0.780000         X3         9.000000          0.120000         X4         0.000000          0.000000       Row    Slack or Surplus     Dual Price         1          0.000000          1.000000         2          0.000000          0.000000         3          2.000000          1.250000         4          1.000000          0.900000         5          0.000000          0.000000 The optimal value of the first decision variable is

For the next three questions, consider the following information for an item for which you must develop an inventory policy.  Annual demand:                         4000 units                                  Order cost:                                  $50 per order                            Per unit holding cost / year:      25% of unit purchase price    Per unit purchase cost:              $10.00 if order quantity < 1000 units                                                       $ 9.50 if 1000 5000 units The only “candidate” order quantities that need to be considered for the best overall answer would be

A retailer purchases a given item from a supplier and then sells the product to its customers.  The following data are estimated for the item under consideration.  Take ALL intermediate computations to the FOURTH decimal place. Annual demand = 5000                                                 Holding cost = $4 / unit / year Working days per year = 200 days                               Order cost = $50 Average daily demand = 25 units                                 Average lead time = 6 days Standard deviation of daily demand = 3 units             Standard deviation of lead time = 1.5 days If the best order quantity was 500, and if you didn’t carry any safety stock, the average inventory level would be…

Consider the following information for an item for which you must develop an inventory policy.  Annual demand:                         4000 units                                  Order cost:                                  $50 per order                            Per unit holding cost / year:      25% of unit purchase price    Per unit purchase cost:              $10.00 if order quantity < 1000 units                                                       $ 9.50 if 1000  5000 units If the best answer was 1000 for this problem, which of the following would be the lowest total cost?

For the next two questions, suppose you had the following output from LINGO for some linear program.    Variable            Value      Reduced Cost         X1         6.000000          0.400000         X2         0.000000          0.780000         X3         9.000000          0.120000         X4         0.000000          0.000000       Row    Slack or Surplus     Dual Price         1          0.000000          1.000000         2          0.000000          0.000000         3          2.000000          1.250000         4          1.000000          0.900000         5          0.000000          0.000000 Which constraints are binding?

It takes the planet Jupiter 12 years to orbit the Sun once. What is the average distance from Jupiter to the Sun? (The distance from the Earth to the Sun is 1.5 x 1011 m.)