2) The Kalo fertilizer company makes a fertilizer using two chemicals that provide nitrogen, phosphate, and potassium. A pound of ingredient 1 contributes 10 ounces of nitrogen and 6 ounces of phosphate, while a pound of ingredient 2 contributes 2 ounces of nitrogen 6ounces of phosphate and 1 ounce of potassium and 1 ounce of potassium. Ingredient 1costs $3 per pound, andingredent2 cost $5 per pound. The fertilizer want to know how many pounds of each chemical ingredient to put into bag of fertilizer to meet the minimum requirement of 20 ounces of nitrogen, 36 ounces of phosphate and 2 ounces of potassium while minimizing cost.
A )Formulate a linear programming model for this problem
B) Solve this model by using graphical analysis
3) Solve the model formulated in the problem 7 for southern sporting Goods Company graphically.
A) Identify the amount of unused resources (ie., slack) at each of graphical extreme points
b) What would be the effect on optimal solution if the profit for a basket ball change from $12 to $13? What would be the effect if the profit for a foot ball changes from $16 to $15?
c) What would be the effect on the optimal solution if 500 additional pounds of rubber could be obtained?. What would be the effect if 500 additional square feet of leather could be obtained?
Southern sporting Goods Company makes basketballs and footballs. Each product is produced from two resources rubber and leather. The resource requirements for each product and the total resources available are as follows.
resource requirement per unit
product
Rubber (Ib)
Leather (ft.2)
Basket ball
3
4
Football
2
5
total resources available
500Ib,
