MAT 540 MAT540 Week 7 Homework

Sporting Goods

(a) Resource Requirements per Unit(c-1) Resource Requirements per Unit

ProductRubber (lb.)Leather (ft²)ProductRubber (lb.)Leather (ft²)

Basketball2,83,7Basketball2,83,7

Football1,55,2Football1,55,2

(a) Hours/ Unit

ProductLine 1Line2

A115

B69

(b)Sensitivity Range for the coefficient of # of units of product A in the objectivefunction

Sensitivity Range for the coefficient of # of units of product B in the objectivefunction

(c')Shadow Price  for additional hours of production time on Line 1

Shadow Price  for additional hours of production time on Line 2

Which one of the two  the company would prefer (Line 1 or Line 2?)

Irwin textile mills

(a)Corduroydenim

Profits for each product3,252,5

ResourcesAvailable Resources

Cotton866000<=6500

Labor433000<=3000

Demands

Corduroy0<=510

denim1000<=1000000

Write the standard form of the LP model in the space provided below

(b)How much extra cotton and processing time are left at the optimal solution?

('c)If Irwin Mills can obtain additional cotton or processing time, but not both, which should it select? How much?

Bradley Family

(a)Let X1 = # of acres of corn and X2 = # of acres of tobacco

(b)How many acres of farm land will not be cultivated at the optimal solution? 

Do the Bradleys use the entire 100 acre tobacco allotment?

('c)Should the Bradleys' lease extral land from their neighbor at $110 per acre? 

What is the maximum price the Bradleys' should pay their neighbor?  And how much land shoud they lease?

(d) For each dollar they borrow , how much additional profit will they make?

If they borrowed a additional $1000, would the number of acres of corn and tobacco they plant change?