Question #$3$: A sporting goods company makes basketballs and footballs. Each product

is produced from two resources $-$ rubber and leather. The resource requirement for

each product and the total resources available are as follows:

Each basketball produced results in a profit of $$12,$ and each football earns $$16$ in profit.

a$.$ Formulate a LP model to determine the number of basketballs and footballs to

produce in order to maximize profit.

b$.$ Solve the model graphically.

c$.$ Identify the amount of unused resources at each of the graphical extreme points.

d$.$ What would be the effect on the optimal solution if the profit for a basketball

changed from $$12$ to $$13?$

e$.$ What would be the effect on the optimal solution if the profit for a football

changed from $$16$ to $$15?$

f$.$ Determine the sensitivity ranges for the available resources using graphical

analysis.

g$.$ Solve the problem by Excel Solver. Provide the model, solution and sensitivity

reports.

h$.$ Comment on the answer and sensitivity reports, and your solutions in parts a$-$f$.$

Question #$4$: Company C produces a chemical mixture for a specific customer in $1,000$

pound batches. The mixture contains $3$ ingredients $-$ zinc, mercury and potassium. The

mixture must conform to formula specifications that are supplied by the customer. The

company wants to know the amount of each ingredient it needs to put in the mixture

that will meet all the requirements of the mix and minimize total cost.

The customer has supplied the following formula specifications for each batch of

mixture:

The mixture must contain at least $200$ pounds of mercury

The mixture must contain at least $300$ pounds of zinc

The mixture must contain at least $100$ pounds of potassium

The ratio of potassium to the other two ingredients cannot exceed $1$ to $4.$

The cost per pound of mercury is $$400$; the cost per pound of zinc, $$180$; and the cost

per pound of potassium, $$90.$

a$.$ Formulate an LP model for this problem

b$.$ Solve model by Excel.

c$.$ Comment on the answer and sensitivity reports. please answer all questions and show all answers and graphs clearly and provide the answers in excel file when asked