Texteriles Company creates different types of bolts of cloth. These bolts of cloth are made on the same machinery. The textile machines have the capacity of 3,600 hours per month. Texteriles is considering producing three different types of cloth: denim, chenille, and gauze, with contribution margins per bolt of $14, $22, and $9, respectively. Texteriles knows it can sell only a total of 6,000 bolts of denim, 2,000 bolts of chenille, and/or 1,200 bolts of gauze. A bolt of each type of cloth requires a different amount of machine time as follows: denim takes 0.5 machine-hours, chenille takes 1 machine-hour, and gauze takes 0.3 machine-hours. What combination of products will maximize the profits of Texteriles

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Sam1s Sam1s · Answer 1 · 2020-10-14T06:10:30+02:00

Answer:

Combination of products shall be:

Denim = 6,000 bolts

Chenille = 240 bolts

Gauze = 1,200 bolts

Explanation:

As provided the machine hours are limited thus, the constraint is machine hours.

Accordingly contribution per machine hour shall be computed.

Denim has contribution of $14 for each 0.5 machine hour, thus, contribution per hour = [tex]\frac{14}{0.5} = 28[/tex]

Chenille has contribution of $22 per machine hour

Gauze has contribution of $9 per 0.3 hours, thus contribution per machine hour = [tex]\frac{9}{0.3}[/tex] = $30

According to contribution per hour, ranking of products shall be

Gauze I

Denim II

Chenille III

Therefore, bolts of gauze to be produced = 1,200 that is maximum

Hours required = 1,200 [tex]\times[/tex] 0.3 = 360

Hours remaining = 3,600 - 360 = 3,240

Bolts of Denim to be produced = 6,000 that is maximum

Hours required = 6,000 [tex]\times[/tex] 0.5 = 3,000

Hours remaining = 3,240 - 3,000 = 240

Bolts of Chenille that can be produced = [tex]\frac{240\ hours}{1\ bolt\ per\ hour}[/tex] = 240 bolts

Total contribution in this case

= (1,200 [tex]\times[/tex] $9) + (6,000 [tex]\times[/tex] $14) + (240 [tex]\times[/tex] $22)

= ($10,800 + $84,000 + $5,280)

= $100,080