Optimization problem

A new burger chain, the EcoliExpress, has has two new products: the large 1/3 pound "Big Whoopie burger and the smaller 1/4 pound "Wimpy Whoopie" burger. It has been determined in test market trials that the Big Whoopie can be sold at a profit of 45 cents per burger and the Wimpy Whoopie at a profit of 25 cents. Furthermore, a chain knows that it can sell all its burgers if it uses 100 pounds of meat per week. In addition, the preparation time for a Big Whoopie is two minutes and for a Wimpy Whoopie is one minute and the chain has one employee working 40 hours per week preparing both types of Whoopies. Assuming the owner of the EcoliExpress wishes to maximize profits formulate a solution using linear programming. Using this model, answer the following: (a) How many Big Whoopies and Wimpy Whoopies should be sold? (b) Assuming the unit profit of the Big Whoopie is fixed at 45 cents, for what range of prices of the Wimpy Whoopie is the solution in a) optimal? (c) Assuming the unit profit of the Wimpy Whoopie is fixed at 25 cents, how large does the unit profit for the Big Whoopie have to be to justify making only this type of burger? (d) What should the cost of meat be (per pound) to justify purchasing additional quantities? Hint: the profit must increase. A new burger chain, the EcoliExpress, has has two new products: the large 1/3 pound "Big Whoopie burger and the smaller 1/4 pound "Wimpy Whoopie" burger. It has been determined in test market trials that the Big Whoopie can be sold at a profit of 45 cents per burger and the Wimpy Whoopie at a profit of 25 cents. Furthermore, a chain knows that it can sell all its burgers if it uses 100 pounds of meat per week. In addition, the preparation time for a Big Whoopie is two minutes and for a Wimpy Whoopie is one minute and the chain has one employee working 40 hours per week preparing both types of Whoopies. Assuming the owner of the EcoliExpress wishes to maximize profits formulate a solution using linear programming. Using this model, answer the following: (a) How many Big Whoopies and Wimpy Whoopies should be sold? (b) Assuming the unit profit of the Big Whoopie is fixed at 45 cents, for what range of prices of the Wimpy Whoopie is the solution in a) optimal? (c) Assuming the unit profit of the Wimpy Whoopie is fixed at 25 cents, how large does the unit profit for the Big Whoopie have to be to justify making only this type of burger? (d) What should the cost of meat be (per pound) to justify purchasing additional quantities? Hint: the profit must increase