In preparation for the winter season, a clothing company is manufacturing parka and goose overcoats, insulated pants, and gloves. All products are manufactured in four different departments: cutting, insulating, sewing, and packing. The company has received firm orders for its products. The contract stipulates a penalty for undelivered items. The following table provides the pertinent data of the situation. Department Parka Goose Pants Gloves Capacity
Cutting 0.30 0.30 0.25 0.15 1000
Insulating 0.25 0.35 0.30 0.10 1000
Sewing 0.45 0.50 0.45 0.22 1000
Packaging 0.15 0.15 0.10 0.05 1000
Demand 800 750 600 500
Unit profit 30 40 20 10
Unit Penalty 15 20 10 8
Formulate the Problem as a LP Problem.

Let A represent no of Parka produced

Let B be number of Goose Produced

Let C be number of Number of Pants

Let D be number of Gloves

A', B', C' and D' are shortages in production if any. The range of these variables will be from 0 to Demand.

Out objective is to plan our production to maximize net profit (Profit-Penalty).

Maximize

P = 30A + 40B + 20C + 10D - 15A' - 20B'  - 10C' - 8D'

s.t

0.3A + 0.3B + 0.25C + 0.15D ≤ 1000

0.25A + 0.35B + 0.30C + 0.10D ≤ 1000

0.45A + 0.50B + 0.40C + 0.22D ≤ 1000

0.15A + 0.15B + 0.10C + 0.05D ≤ 1000

0 ≤ A'  ≤ 800

0 ≤ B'  ≤ 750

0 ≤ C'  ≤ 600

0 ≤ D'  ≤ 500

bd = 9 cm

step-by-step explanation:

in a 30°-60°-90° triangle, the ratio of side lengths is 1 : √3 : 2. that is, the longest side (hypotenuse) is twice the length of the shortest side.

all of the triangles in your geometry are 30°-60°-90° triangles. ac is the hypotenuse of δacd, and the short side of δabc.

the short side ad of δacd will be half the length of ac, so 3 cm. the hypotenuse ab of δabc will be twice the length of ac, so 12 cm. segment bd is the difference of the lengths ab and ad, so is

bd = ab -ad

bd = 12 cm - 3 cm = 9 cm

comment on side length ratios

you can figure the ratios of side lengths in a 30°-60°-90° triangle by considering the trig ratios of the angles. or you can figure the length of the altitude of an equilateral triangle of side length 2 using the pythagorean theorem.

convection currents in magma drive plate tectonics. the answer is true.