Solutions to Sensitivity Questions

Tucker Automobiles

  1. Produce 400 at 1, 200 at 2, and 400 at 3, for a cost of $11,600,000.
  2. It costs $30,000 to produce one more, saves $30 to produce 1 less.
  3. Production remains the same, so we same $2,000(200)=$400,000. This type of analysis is valid for any cost of at least $8000.
  4. Nothing
  5. It is costing us $4,000 per car that must be produced. Value of reducing to 200 cars is $800,000; value of reducing to 0 cars is $1,600,000. Cost of increasing by 100 cars is $400,000. Increasing by 200 cars is outside range, but total cost is at least $800,000.
  6. Material is worth $5,000 per unit. We are willing to buy 300 units at that price. After that we will be willing to spend an unknown (but lower) amount per unit.
  7. Producing such a car costs us $20,000 worth of material, but saves us the marginal $30,000 of producing with our current plants. Therefore the cost can be no more than $10,000.
  8. It must reduce its cost to 0 for us to consider it. Alternatively, it could reduce its material usage to 4.6.
  9. It doesn't matter how expensive it gets, we will always produce at plant 1 (due to our extreme material shortage).

Map Production

  1. Quantities of A, B, C, and D are 1500, 1000, 1000, 2833.33 respecitvely, for a profit of $10,166.67
  2. .50 for printing, 0 for cutting, .167 for folding. 1000 hours for printing, no limit for cutting, and 7000 hours for folding.
  3. Either B or C. Profit improves by 100(.333) = $33.33.
  4. 2 minutes to print costs $1, 2 minutes to cut cost $0, 3 minutes to fold costs $0.50, so the profit must be at least $1.50. You cannot tell the effect of requiring 1000 without rerunning.
  5. Knowing the cost more accurately will not change the production decision. Since the total effect is $0.25 (2833) = $708, it seems unlikely that knowledge is worth $500.