Apple Inc., must determine how many new Apple Watch to produce each of

the next four quarters of $2023.$ The demand for each of the next four

quarters is as follows: first quarter, $6000$ Watches; second quarter,

$5500$ Watches; third quarter, $7500$ Watches, fourth quarter, $6500$

Watches. Apple must meet demand on time. At the beginning of the first

quarter, Apple Inc., has an inventory of $450$ Watches. At the beginning

of each quarter, Apple Inc., must decide how many Watches should be

produced during that quarter. For simplicity, we assume that Watches

manufactured during a quarter can be used to meet demand for that

quarter.

During each quarter, Apple Inc., produces up to $3500$ Watches with

regular$-$time labor at a total cost of $$200$ per Watch. By having

employees work overtime during a quarter, Apple Inc., can produce

additional Watch with overtime labor at a cost of $$300$ per Watch. At

the end of each quarter $($after production has occurred and the current

quarter$$s demand has been satisfied$),$ a carrying or holding cost of

$$10$ per Watch is incurred. Formulate the linear programming to

determine a production schedule to minimize the sum of production and

inventory costs during the next four quarters. $($Attach Excel Solution

showing model display and screen shot of solver$)$Apple Inc., must determine how many new Apple Watch to produce each of

the next four quarters of $2023.$ The demand for each of the next four

quarters is as follows: first quarter, $6000$ Watches; second quarter,

$5500$ Watches; third quarter, $7500$ Watches, fourth quarter, $6500$

Watches. Apple must meet demand on time. At the beginning of the first

quarter, Apple Inc., has an inventory of $450$ Watches. At the beginning

of each quarter, Apple Inc., must decide how many Watches should be

produced during that quarter. For simplicity, we assume that Watches

manufactured during a quarter can be used to meet demand for that

quarter.

During each quarter, Apple Inc., produces up to $3500$ Watches with

regular$-$time labor at a total cost of $$200$ per Watch. By having

employees work overtime during a quarter, Apple Inc., can produce

additional Watch with overtime labor at a cost of $$300$ per Watch. At

the end of each quarter $($after production has occurred and the current

quarter$$s demand has been satisfied$),$ a carrying or holding cost of

$$10$ per Watch is incurred. Formulate the linear programming to

determine a production schedule to minimize the sum of production and

inventory costs during the next four quarters. $($Attach Excel Solution

showing model display and screen shot of solver$)$