Question

Product	Cutting	Sewing	Material
Skirt	1	1	1
Dress	4	3	1
Sport Coat	6	6	4

The? Trim-Look Company makes several lines of? skirts, dresses, and sport coats.? Recently, a consultant suggested that the company reevaluate its South Islander line and allocate its resources to products that would maximize contribution to profits and to overhead. Each product requires the same polyester fabric and must pass through the cutting and sewing departments. The following data were collected for the study.

The cutting department has 100 hours of? capacity, sewing has 150 hours of? capacity, and 60 yards of material are available. Each skirt contributes $8 to profits and? overhead; each? dress, ?$16 and each sport? coat, $40

Let X1? = number of skirts? produced, X 2 = number of dresses? produced, X3 = number of sport coats produced.

a Specify the objective function and contraints for the problem

b. A linear programming software shows the optimal solution? as:

X1 equals=0

X2 equals=4

X3 equals=14

How much would you be willing to pay for an extra hour of cutting? time?

You would be willing to add an extra hour of cutting time if its cost were less than _____enter your response rounded to the nearest? cent Please show detail on how to set up in Solver

Answer 1

Decision variable: as shown in green in fig1

Let X1? = number of skirts? produced,

X2 = number of dresses? produced,

X3 = number of sport coats produced.

Objective function: as shown in fig1 in yellow

Maximize profit:

8*X1 + 16*X2 + 40*X3

In excel: C11 = SUM(C8:C10)

C8 = B8*B2, similarly C9 and C10

Constraints:

1. Cutting: Maximum 100 hours available

1*X1 + 4*X2 + 6*X3 100, in excel: D5 =SUM(D2:D4), D2 = C2*B2, similarly D3 and D4,

constraint in fig2: D5 100

2. Sewing maximum 150 hours

1*X1 + 3*X2 + 6*X3 150, in excel: F5 =SUM(F2:F4), F2 = E2*B2, similarly F3 and F4,

constraint in fig2: F5 150

3. Material: maximum 60 yards

1*X1 + 1*X2 + 4*X3 60, in excel: H5 =SUM(H2:H4), H2 = G2*B2, similarly H3 and H4,

constraint in fig2: H5 60

4. X1,X2,X3 0

SOlving this model in excel: as shown in fig1 and fig2

we get:

X1 equals=0

X2 equals=4

X3 equals=14

fig1

fig2

You would be willing to add an extra hour of cutting time if its cost were less than 2.4 (as shown in fig3 below in sensititvity report.)

the shadow price in sensitivity report shows the contribution of the constraint in the profit. Hence 1 unit of increase of cutting will add 2.4 to the profit. Hence maximum the company should pay for cutting extra hour is 2.4. This is valid till 90 hours of increase.

fig3