Question

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. what is the objective function?

Answer 1

In an optimization model, the objective function represents the target of the company (either a maximization of minimization). In this case, the company's aim is to maximize profit. If the company gets $0.40 of profit per box of deluxe crackers (d), and $0.50 of profit per box of classic crackers (c), then its objective function will be the total profit from the deluxe and classic crackers. This gives the objective function Z = 0.4d + 0.5c.

The rest of the given, such as the available supply of ingredients and the formulation details, are used as constraints in the optimization model.

Answer 2

For this case, the first thing we are going to do is define variables:
d: deluxe crackers
c: classic crackers
x: ounces of sugar
y: ounces of flour
z: ounces of salt
The obtetive function is to maximize the production:

`z = 0.40d + 0.50c`
It is subject to the following restrictions:
ounces of sugar:

`2x + 3x \leq 4800`
ounces of flour:

`6y + 8y \leq 9600`
ounces of salt:

`z + 2z \leq 2000`
Answer:
the objective function is:
maximize production:

`z = 0.40d + 0.50c`