Question :
7.MegaSports, Inc. produces two highpriced metal baseball bats, the Slugger : 1825500
7.MegaSports, Inc. produces two highpriced metal baseball bats, the Slugger and the Launcher, that are made from special aluminum and steel alloys. The cost to produce a Slugger bat is $100, and the cost to produce a Launcher bat is $120. We can not assume that MegaSports will sell all the bats it can produce. As the selling price of each bat model  Slugger and Launcher  increases, the quantity demanded for each model goes down.
Assume that the demand, S, for Slugger bats is given by S = 640 ? 4P_{S} and the demand, L, for Launcher bats is given by L = 450 ? 3P_{L}_{ }where P_{S} is the price of a Slugger bat and P_{L} is the price of a Launcher bat. The profit contributions are P_{S }S ? 100S for Slugger bats and P_{L }L ? 120L for Launcher bats. Develop the total profit contribution function for this problem.
8.PacificGulf Oil Company is faced with the problem of refining three petroleum components into regular and premium gasoline in order to maximize profit. Components 1 and 2 are pooled in a single storage tank and component 3 has its own storage tank. Regular and premium gasolines are made from blending the pooled components and component 3. Prices per gallon for the two products and three components, as well as product specifications, are listed below.

Price Per Gallon 
Regular gasoline 
$2.80 
Premium gasoline 
3.10 
Component 1 
2.40 
Component 2 
2.50 
Component 3 
2.75 
Product 
Specifications 
Regular gasoline 
At most 25% component 1 

At least 40% component 2 

At most 30% component 3 
Premium gasoline 
At least 30% component 1 

At most 50% component 2 

At least 25% component 3 
The maximum number of gallons available for each of the three components is 4000, 8000, and 8000, respectively. Formulate a nonlinear program to determine: 1) what percentages of component 1 and component 2 should be used in the pooled mixture, and 2) how to make regular and premium gasoline by blending the mixture of components 1 and 2 from the pooling tank with component 3.