Kilgore's Deli is a small delicatessen located near a major university. Kilgore's does a large walk-in carry-out lunch business. The deli offers two luncheon chili specials, Wimpy and Dial 911. At the beginning of the day, Kilgore needs to decide how much of each special to make (he always sells out of whatever he makes). The profit on one serving of Wimpy is $0.55, on one serving of Dial 911, $0.51. Each serving of Wimpy requires 0.5 pound of beef, 0.5 cup of onions, and 5 ounces of Kilgore's special sauce. Each serving of Dial 911 requires 0.5 pound of beef, 0.8 cup of onions, 3 ounces of Kilgore's special sauce, and 5 ounces of hot sauce. Today, Kilgore has 39 pounds of beef, 49 cups of onions, 109 ounces of Kilgore's special sauce, and 75 ounces of hot sauce on hand. a. Develop a linear programming model that will tell Kilgore how many servings of Wimpy and Dial 911 to make in order to maximize his profit today
b. Find an optimal solution.
c. What is the shadow price for special sauce’? Interpret the shadow price.
d. Increase the amount of special sauce available by 1 ounce and re-solve. Does the solution confirm the answer to part (c)? Give the new solution.

The resumâ´es of two male applicants for a college teaching position in chemistry are placed in the same file as the resumâ´es of two female applicants. two positions become available, and the first, at the rank of assistant professor, is filled by selecting one of the four applicants at random. the second position, at the rank of instructor, is then filled by selecting at random one of the remaining three applicants. using the notation m2f1, for example, to denote the simple event that the first position is filled by the second male applicant and the second position is then filled by the first female applicant, (a) list the elements of a sample space s; (b) list the elements of s corresponding to event a that the position of assistant professor is filled by a male applicant; (c) list the elements of s corresponding to event b that exactly one of the two positions is filled by a male applicant; (d) list the elements of s corresponding to event c that neither position is filled by a male applicant; (e) list the elements of s corresponding to the event a â© b; (f) list the elements of s corresponding to the event a âş c; (g) construct a venn diagram to illustrate the intersections and unions of the events a, b, and c.