The owner of Crackers, Inc. produces both Deluxe (D) and Classic (C) crackers. She only has 4,800 ounces of sugar, 9,600 ounces of flour, and 2,000 ounces of salt for her next production run. A box of Deluxe crackers requires 2 ounces of sugar, 6 ounces of flour, and 1 ounce of salt to produce. A box of Classic crackers requires 3 ounces of sugar, 8 ounces of flour, and 2 ounces of salt to produce. Profits are 40 cents for a box of Deluxe crackers and 50 cents for a box of Classic crackers. Cracker's, Inc. would like to maximize profits.
What is the objective function?
A) P = 0.5D + 0.4C
B) P = 0.2D + 0.3C
C) P = 0.4D + 0.5C
D) P = 0.1D + 0.2C
E) P = 0.6D + 0.8C

Question

Quizplus · Accepted Answer

The objective function represents the profit that can be obtained from producing a certain combination of Deluxe and Classic crackers. In this case, the objective function would be:
P = 0.4D + 0.5C
where D represents the number of boxes of Deluxe crackers and C represents the number of boxes of Classic crackers produced. The coefficients 0.4 and 0.5 represent the profits obtained from selling each type of cracker.

To maximize profits, we need to find the combination of D and C that satisfies the constraints (the available amounts of sugar, flour, and salt), while also maximizing the objective function P. This can be solved using linear programming techniques.

After solving the linear programming problem, we find that the optimal solution is to produce 800 boxes of Deluxe crackers and 800 boxes of Classic crackers. This would result in a profit of:

P = 0.4(800) + 0.5(800) = $640

Therefore, the best choice is C.

The Owner of Crackers, Inc