ABC,Inc.,is a small clothing manufacturer that produces shirts and pants using two resources: sewing machine hours and cutting machine hours.The production manager can schedule up to 240 hours of sewing machine time and up to 150 hour cutting machine time.Production of one shirt requires 3 hours of sewing time and 1 hour of cutting time.Each pair of pants requires 2 hours of sewing time and 1.5 hours of cutting time.Each shirt yields a profit of $5,and each pair of pants generates a $6 profit.The objective is to maximize profits.Determine cutting time constraint for the LP formulation.Let X₁ = Number of shirts to be produced,X₂ = Number of pairs of pants to be produced.
A)3X₁ + 2X₂ ≤ 240
B)X₁ + 1.5X₂ ≤ 150
C)3X₁ + 2X₂ ≤ 150
D)X₁ + 1.5X₂ ≤ 240

Question

Quizplus · Accepted Answer

To determine the cutting time constraint for the LP formulation, we need to find the total amount of cutting time required for the production of X₁ shirts and X₂ pairs of pants.

For X₁ shirts, the cutting time required is X₁ hours (1 hour per shirt).

For X₂ pairs of pants, the cutting time required is 1.5X₂ hours (1.5 hours per pair of pants).

Therefore, the total cutting time required is:

Cutting time = X₁ + 1.5X₂

To maximize profits, we need to ensure that the total cutting time required does not exceed the maximum cutting machine time available, which is 150 hours.

Thus, the cutting time constraint for the LP formulation is:

X₁ + 1.5X₂ ≤ 150

Therefore, the best choice is B.

ABC,Inc,Is a Small Clothing Manufacturer That Produces Shirts and Pants