Problem $1.$

Apple Inc must decide how many iPhones $to$ produce $in$ each $of$ the next four quarters. The demand during each quarter $isQ1$: $35k,Q2$: $50k,Q3$: $30k,Q4$: $60.$ Apple must meet demands $on$ time $by$ the end $of$ each quarter. $At$ the beginning $ofQ1$ Apple has $10k$ iPhones $in$ inventory. Apple can produce $upto40k$ iPhones $in$ a quarter with regular production $at$ a cost $of$ $$\frac{200}{p}$hone, $or$ overtime production $at$ a cost $of$ $$\frac{250}{p}$hone. There $isa$ $$50$ holding cost for the remaining inventory $at$ the end $of$ each quarter.

Formulate a linear programming model $to$ meet demand with minimum cost.

a Define variables

$b$ Write the objective function

$c$ Formulate the constraints.