Operations research formulation question

[mikky05v]

I'm not sure where this subject is supposed to go but it seemed to fit better here than in calculus and beyond.

Homework Statement

Formulate the following problem and then use desmos or guess and check to solve it: The magnetic attraction company produces large and small magnets at 2 different factories, with the following daily output.

Location: Port Huron
Large: 80
Small: 100
Location: Boca Raton
Large: 125
Small: 90

Maximize the total number of magnets that can be produced in a ten day period if neither factory can be open more than seven days, the number of large magnets cannot exceed 750, and the number of small magnets cannot exceed 850, Note the plant cannot be opened half of a day.

The Attempt at a Solution

I think three of my constraints would be
100x_{1} +90x_{2} ≤ 850
80x_{1} +125x_{2} ≤ 750
x_{i}>0
but I'm lost on the z, i know I'm supposed to pull it out of the 10 day statement but I don't know what numbers to use. Can someone explain to me how to pull this out of the statement?

 

[mikky05v]

[STRIKE][/STRIKE]attempt 2: trying a strategy used in some solved problems from the book

Objective: maximize the number of magnets, z that can be produced in a 10 day period if neither factory can be open more than 7 days (I don't know how to fit this into the problem, it sounds like a constraint but I don't know how to formulate it)

so z = the number f small magnets times the number of days plus the number of large magnets times the number of days.
but then my variables x_{1} and x_{2} are both the number of days and I know the number of days to be 10 so this doesn't make sense.

the variables have to be the number of days factory 1 is open and the number of days factory 2 is open and somehow it needs to pull in the fact that they can't be open more than 7 days.

 

[Mark44]

In a bit more detail, x₁ is the number of days that the Port Huron factory operates, and x₂ is the number of days that the Boca Raton factory operates.

Since neither factory can be open more than 7 days in the 10-day period, you have two more constraints.