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

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?

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…

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.)

p2something.png An object side a distance d down and incline of height ∆y as shown.  If the coefficient of friction between the surface and the object is 0.250, determine the work done by friction. m = 5.00 kg, d = 9.00 m,  and ∆y = 3.00 m.

A worker pushes a 8.0 kg crate across a level surface with a force of 35.0 N directed at an angle of 25.0° downward from the horizontal. Determine the work done by gravity after the crate is pushed 12.0 m.

What is the kinetic energy of a car of mass 1750 kg traveling at 25 m/s?

The force on an electric charge in an electric field is F = qE where F is the force, q is the electric charge, and E is the electric field.  Determine the speed of a proton (charge = 1.6×10-19 C, mass = 1.67×10-27 kg) after it has been accelerated, from rest, a distance of 0.25 m though an electric field of 2.0×106 N/C.