A linear programming computer package is needed.

Frandec Company manufactures, assembles, and rebuilds material$-$handling equipment used in warehouses and distribution centers. One product, called a

Liftmaster, is assembled from four components: a frame, a motor, two supports, and a metal strap. Frandec's production schedule calls for $5,500$ Liftmasters to be

made next month. Frandec purchases the motors from an outside supplier, but the frames, supports, and straps may be either manufactured by the company or

purchased from an outside supplier. Manufacturing and purchase costs per unit are shown.

Three departments are involved in the production of these components. The time $($in minutes per unit$)$ required to process each component in each department and

the available capacity $($in hours$)$ for the three departments are as follows.

$($a$)$ Formulate and solve a linear programming model for this make$-$or$-$buy application. $($Let $FM=$ number of frames manufactured, $FP=$ number of frames

purchased, $SM=$ number of supports manufactured, $SP=$ number of supports purchased, $TM=$ number of straps manufactured, and $TP=$ number of straps

purchased. Express time in minutes per unit.$)$

Min $37FM+50FP+10\mathrm{.}5SM+14SP+5\mathrm{.}5TM+6\mathrm{.}5TP$

Cutting constraint

Milling constraint

Shaping constraint

$x$

$x$

Frame constrain

$x$

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Min $37FM+50FP+10\mathrm{.}5SM+14SP+5\mathrm{.}5TM+6\mathrm{.}5TP$ A linear programming computer package is needed.

Frandec Company manufactures, assembles, and rebuilds material$-$handling equipment used in warehouses and distribution centers. One product, called a

Liftmaster, is assembled from four components: a frame, a motor, two supports, and a metal strap. Frandec's production schedule calls for $5,500$ Liftmasters to be

made next month. Frandec purchases the motors from an outside supplier, but the frames, supports, and straps may be either manufactured by the company or

purchased from an outside supplier. Manufacturing and purchase costs per unit are shown.

Three departments are involved in the production of these components. The time $($in minutes per unit$)$ required to process each component in each department and

the available capacity $($in hours$)$ for the three departments are as follows.

$($a$)$ Formulate and solve a linear programming model for this make$-$or$-$buy application. $($Let $FM=$ number of frames manufactured, $FP=$ number of frames

purchased, $SM=$ number of supports manufactured, $SP=$ number of supports purchased, $TM=$ number of straps manufactured, and $TP=$ number of straps

purchased. Express time in minutes per unit.$)$

Min

Cutting constraint

Milling constraint

Shaping constraint

Frame constraint