1. Which of the following mathematical relationships could be found in a linear programming model and which could not? For the relationships that are unacceptable for linear programs, state why. Recall that only linear functions can be in linear programs. (5 points)
   1. –A + 2B <= 70
   2. 2A – 2B = 50
   3. A – 2B ² <= 10
   4. A + B = 6
   5. 2A + 5B + AB <= 25
2. Plot the feasible region which satisfies all of the following constraints: (2 points)
   1. X >= 3
   2. Y <= -2
   3. X <= 5
   4. Y >= -4
3. Compute the value of the objective function (3x-7y) for each of the corner points of problem 2. (2 points)
4. The Sea Wharf Restaurant would like to determine the best way to allocate a monthly advertising budget of $1000 between newspaper advertising and radio advertising. Management decided that at least 25% of the budget must be spent on each type of media, and that the amount of money spent on local newspaper advertising must be at least twice the amount spent on radio advertising. A marketing consultant developed an index that measures audience exposure per dollar of advertising on a scale from 0 to 100 with higher values implying greater audience exposure. If the value of the index for local newspaper advertising is 50 and the value of the index for spot radio advertising is 80, how should the restaurant allocate its advertising budget in order to maximize the value of total audience exposure? (13 points)

1. What is the objective function (maximize or minimize what quantity) in words? (1 point)
2. What are the two decision variables? (1 point)
3. What are the constraints in words? Remember that you can’t spend a negative amount. (2 points)
4. Write the objective function mathematically. (1 point)
5. Write the constraints mathematically. (2 points)
6. Solve the problem either graphically or (strongly recommended) using Excel. Report the optimal values of the decision variables. (5 points)
7. Report the optimal value of the objective function. (1 point)
   5. The New England Cheese Company produces two cheese spreads by blending mild cheddar cheese with extra sharp cheddar cheese. The cheese spreads are packaged in 12-ounce containers which are then sold to distributors. The Regular blend contains 80% mild cheddar and 20% extra sharp. The Zesty blend contains 60% mild cheddar and 40% extra sharp. This year a local dairy cooperative offered to provide up to 8100 pounds of mild cheddar cheese for $1.20 per pound and up to 3000 pounds of extra sharp cheddar cheese for $1.40 per pound. The cost to blend and package the cheese spreads, excluding the cost of the cheese, is $0.20 per container. If each container of Regular is sold for $1.95 and each container of Zesty is sold for $2.20, how many containers of Regular and Zesty should New England Cheese produce? (13 points)
   1. What is the objective function (maximize or minimize what quantity) in words? (1 point)
   2. What are the two decision variables? (1 point)
   3. What are the constraints in words? Remember that you can’t produce a negative amount. (2 points)
   4. Write the objective function mathematically. (1 point)
   5. Write the constraints mathematically. (2 points)
   6. Solve the problem either graphically or (strongly recommended) using Excel. Report the optimal values of the decision variables. (5 points)
   7. Report the optimal value of the objective function. (1 point)

6. In the spreadsheet "DietProblem.xls", look at the "model" tab and open the solver menu. You will see four sets of constraints:

• D9:D19 <= B9:B19 (this means D9 <= B9 and D10 <= B10 and D11 <= B11 and so on)

• D9:D19 >= A9:A19

• G5:BR5 <= G4:BR4

• G5:BR5 >= G3:BR3

The values in blue are the decision variables. The values in yellow are the calculated costs and nutrient values in the foods based on the number of servings selected in row 5. Note that the prices are a few decades old.

1. What do the values in cells D9:D19 represent? (2 points)
2. What does the value of cell D8 represent? (1 point)
3. Explain the meaning of the four types of constraints. (4 points)
4. Solve for the optimal solution. Would you like to plan your daily diet according to this solution? (1 point)

Price: $21.6

Solution: The downloadable solution consists of 10 pages, 1160 words and 1 charts.
Deliverable: Word Document