Need help on Maximizing Profit

[XTerryX]

Maximizing Profit

The local Deli needs to maximize their profit on menu items based on labor rates.
The three main sources of labor include i) cutting vegetables, ii) assembling, and iii) garnishing.
Currently, the main menu items are submarine sandwiches and pasta salads, each yielding a profit of
$1.50 and $1.75, respectively. Given that each task has 11, 9, and 7 hours of total labor effort available,
and given the following table, answer the following questions.

Sub Sandwiches(by the dozen) Pasta Salads(by the dozen)
Cutting Vegetables 0.5 hours 0.5 hours
Assembling 0.5 hours 0.75 hours
Garnishing 0.5 hours 0.75 hours


(1) Given that the store is trying to maximize their profit based on how many submarine sandwiches and
pasta salads they should make, determine the objective function of this scenario.

(2) Expand the table, and fill in any other necessary information needed to solve this
maximization problem.

(3) Use Excel Solver and generate an answer report to solve the problem.

(4) Did you find an optimal solution to the problem? When does it occur?

(5) Suppose the Deli speeded up their time for garnishing by 10 minutes for making submarine
sandwiches. How would your solution change? What if it speeded up by 15 minutes for submarine
sandwiches and slowed down by 15 minutes for pasta salads?

I haven't touched this stuff for a while, and my friend ask me for help. I am kinda lost, any help would be great (profit equation, etc...) Thanks.

 

[HallsofIvy]

Have you ever touched "linear programming"? It is rather a specialized field!

In any case, tell your friend to review all of the definitions relating to things like this, give it a good hard TRY and post what he has tried here. It is much easier to make useful suggestions if we can see what he does or doesn't know about this problem.

 

[CRGreathouse]

Assuming you must make the foods by the dozen, the problem is so small that it doesn't really need a solver at all -- it would be easy to test all possibilities in Excel, and not too hard by hand.

So what's hard for you? The problem seems straightforward -- an easy case of integer programming, as I read it.