The Fast Food Fantasy (Triple-F) hamburger chain is attempting to respond to customer demand for more healthy food by introducing a new birdburger made from a combination of beef and chicken. The new burger should weight at least 125 grams and have at most 350 calories, 15 grams of fat, and 360 milligrams of sodium. Each gram of beef used has 2.5 calories, 0.2 gram of fat, and 3.5 milligrams of sodium. Corresponding values for chicken are 1.8 calories, 0.1 gram, and 2.5 milligrams.

Triple-F wants to find the mix that will meet all requirements and maximize beef content.

(a) Formulate a mathematical programming model to decide an optimal birdburger blend using decision variables x1!grams of beef per burger and x2!grams of chicken per burger.

(b) Enter and solve your model with the class optimization software.

(c) Using a two-dimensional plot, solve your model graphically for an optimal ingredient mix, and explain why it is unique.

(d) On a separate 2-dimensional plot, show graphically that the model becomes infeasible if weight requirement is raised from 125 grams to 200 grams.

(e) On a separate 2-dimensional plot, show graphically that the model is unbounded if the minimum weight and nonnegativity constraints are omitted.