Word Problem: Three new products are to be produced.

[ashlee12]

How do I formulate this?

Three new products are to be produced.
Total production should range between 1,000 and 2,000 units
At least 1 item of product 2 is made for every item of product 1
The total production of product 1 and product 2 should be half the production of product 3
The first 12 units of product 1 earn $17/unit, additional units earn $15/unit.
Product 2 earns $10/unit
The frist 5 units of product 3 earn $20/unit, the next 15 units earn $18/unit, the next 2,000 units earn $9/unit


I need the variables defined and then the z equation of min or max, the functional constrainsts, and non-negativity constrainsts.

 

[arthur ohlsten]

let P1 be the number of units of product 1
let P2 be the number of units of product 2
let P3 be the number of units of product 3

eq1 1000<[P1+P2+P3]<2000
eq2 p2>=P1
eq3 P3=2[P1+P2]
eq4 revenue P1= P1[$17] 0<p1<=12
=$15[ P1-12] 12<P1
eq5 revenue P2=$10P2
eq6 revenue P3=$20P3 0<P3<6
=$18[P3-5] 5<P3<21
=$9[P3-20] 20<P3 P3 will be less than 2000 by eq1

Arthur

are you to solve this for the optimum amounts?

 

[stapel]

How do I formulate this?

How do you formulat what? There is not actual question in the posted exercise.

Thank you.

Eliz.

 

[stapel]

I need the variables defined and then the z equation of min or max, the functional constrainsts, and non-negitivity constrainsts.

You learned how to pick variables back in algebra, so that shouldn't be a problem. Once you've done that, the non-negativity constraints are a simple matter of writing inequalities to reflect the fact that you cannot negative numbers of units.

What do you mean by "the z equation"? Is that the optimization equation?

When you reply, please show all of your work and reasoning so far. Thank you.

Eliz.