I need help solving this:
In order to obtain maximum profit, how many should be bought?
regular head screws: cost is $10 per dozen, the profit over cost is $15 per dozen
phillips head screws: cost is $4 per dozen, the profit over cost is $8 per dozen.
OK, putting in the profit over cost solves that little problem.
Joe can order no more than 40 dozen screws combined
Minimum of 10 dozen philips head must be orderd
Joe cannot order more than $400 worth of regular and phillips head screws
use linear programming to find out how many screws of each shuld be ordered.
Start by defining the relevant variables and assigning a unique letter to each. Hint: there are three relevant variables.
x=regular screws in dozens. It may be important to remember that we are dealing in dozens so WRITE IT DOWN.
y= phillips in dozens. It may be important to remember that we are dealing in dozens so WRITE IT DOWN.
But the really critical thing is that you identified two of the three relevant variables on your own. Good thinking.
I am not sure about the other one i think it should be cost No. The problem asks you to maximize profit, right? The cost is put in there as an extraneous detail. It may annoy you that extraneous details are inserted into a problem, but I ASSURE you that, in real life, problems come loaded with unnecessary details. One of the useful things about word problems is that they require you to separate the essential from the irrelevant. So you need a variable for profit. Let's say z = profit.
Next, express, using the letters assigned to each variable, each constraint imposed by the problem as an inequation.
x+y> 40 This is wrong, but not crazy wrong.The problem says that Joe can order "no more" than 40 dozen screws of both kinds combined, right? Your inequation says that he must order at least 40 dozen. The correct constraint is
\(\displaystyle x + y \le 40\), do you see why? This was probably a careless error; at worst, you were on the right track.
Are there any other constraints that the problem gives EXPLICITLY? If so, what are they and how do you express them mathematically? My next question may seem like a trick question, but it is typical of problems in linear programming. Are there any constraints that are logically required, but not explictly given in the problem? In your course material is there any mention of non-negativity constraints?
Third, express, using the letters assigned to each variable, the objective
function.
If the terms "constraint" and "objective function" are mysterious to you, please let us know EXACTLY how are they defined in your course materials and what you find obscure about those definitions?
