1. A farmer has 10 acres to plant in wheat and barley. He has to plant at least 7 acres .However, he has only $1200 to spend and each acre of wheat costs $200 to plant and each acre of barley cost $100 to plant. Moreover, the farmer has to get the planting done in 12 hours and it takes an hour to plant an acre of wheat and 2hrs to plant an acre of barley. If the profit is $500 per acre of wheat and $300 per acre of barley how many acres of each should be planted to maximize profits? Construct the Linear Programming model.
2. Assume that the BP rig in the Gulf of Mexico has four safety devices all connected in a series. The corresponding reliabilities of these devices are:
Device 1: .85
Device 2: .95
Device 3: .80
Device 4: .80
Furthermore, device 3 has a backup system with two components each with reliability of .50.What is the likelihood that these safety devices (working together)will prevent another disaster?
3. Draw a graph to show the costs of preventive maintenance and breakdown maintenance as a function of maintenance commitment. How do you solve for the lowest total maintenance cost? Just describe the general approach.
4. Based on available information, the lead time demand for component A averages 50 units (normally distributed with standard deviation of 5 units. Your boss wants a 97% service level. How many units of A should be carried as safety? What is the appropriate reorder point?
5. Your distribution company has an annual demand of 1,400 lawn mowers. The cost of a lawn mower to you is $400.carrying cost is estimated to be 20%of unit cost and the ordering cost is $25 per order. If you order in quantities of 300 or more, you can get a 5% discount. Should you take the quantity discount?
6. Outsourcing Analysis.
Your company sells riding gloves and has the following three options
Option 1: Make your own gloves at your own plant. Fixed cost at own plant =$3million.Variable cost /pair at own plant =$5
Option 2: Outsource to a supplier in the same town. Fixed cost at supplier's plant =$2million.Variable cost/pair at supplier's plant =$7
Option 3.Buy from China at $4/pair but you need to pay a one-time set up fee of $5 million
Conduct the cross over analysis. Indicate over what range each of the alternatives Option 1, 2, 3 is the low-cost option
7. First, solve the transportation problem below using the intuitive least cost method ,Then use the Northwest corner method to get a feasible starting solution and apply the stepping -stone method to get the optimal solution.
Store AStoreB StoreCSupply
Plant 1 5 34100
Plant 2 8 3 4300
Plant 3 9 57300
Demand 300 200 200700