the weekly production capacities are $5,0006-$cylinder connecting rods and $7,0004-$cylinder connecting rods. Let

$x_4=$ the number of $4-$cylinder connecting rods produced next week

$x_6=$ the number of $6-$cylinder connecting rods produced next week

$s_4=1$ if the production line is set up to produce the $4-$cylinder connecting rods; $0$ if otherwise

$s_6=1$ if the production line is set up to produce the $6-$cylinder connecting rods; $0$ if otherwise

$($a$)$ Using the decision variables $x_4$ and $s_4,$ write a constraint that limits next week's production of the $4-$cylinder connecting rods to either $0$ or $7,000$ units.

$($b$)$ Using the decision variables $x_6$ and $s_6,$ write a constraint that limits next week's production of the $6-$cylinder connecting rods to either $0$ or $5,000$ units.

$($c$)$ Write a third constraint that, taken with the constraints from parts $($a$)$ and $($b$),$ limits the production of connecting rods for next week.

$$

$($d$)$ Write an objective function for minimizing the cost of production for next week.

Min

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