Question

15. The American Company manufacturers artillary shells (A), hand grenades (H), and bullets (B) from the raw materials gunpowder (G), lead (L), and steel (S). The materials are used as shown in percentage of weight in the following table А H The company will have a production run when the supply shipment arrives. There are two possible shipments, which we give in 1000-pound units: 1. G-140, L-30, S-100 2. G-170, L-50, S-110 The company wants to use all materials on the production run. Find the production schedule (amounts of A, H, and B) for each supply possibility. Solve the two problems simultaneously.

Answer 1

1st Problem :

Let x, y and z denote the amounts of A, H and B respectively.

So the equations can be written as

0 0.6% +0-54 +10-52 = 140 0-12 toly + 0-2 Z = 30 - 0-34 + 0.44 +0.32s 100 - 0 © © - Multiply eq © by 2 and subtract from ean 0 -0-34-0-12 = -60 L 30-34 +0-12 = Go - in multiply egr @ by 6 and subtract from eq? 0 --0-1 y - 0-72 -40 0-14 +10-7 z = 40 - ☺ from eq Multiply ear by 3 and subtract - 22 = –60 (Z = 30 | SRB

substitutina z = 30 in ean 4 0-34 + 0.1 X 30 = 60 -:[y = 190] __ _ substituting values of y and z in egn @ 0.1 +0.1 x 190 + 0-2 x 30 = 30 Tzs501 1 the first supply possibility the production schedule should be 50000 artillary shells (A) 190000 hand grenades (H) and 30000 bullets (6) -

2nd Problem :

The equations are written as

0.64 +054 +0.525170 0 0-12 + Only + 0-2 z s 50 — ® 0:32 + 0-44 +0-32s110 - ☺ subtract from eq? 0 Multiply ear ② by 2 and -0-34-0.12 = -50 : 0-34 + 0.1 2 = 50 - - from ego ® >NO multiply egn © by 6 and subtract --0-19-0-72 = -130 0-17 +072 = 130 — 5

and subtract from ea a Multiply eq ② by 3 Pozs-340 2:170 eq substitute z=170 in 0-34 +0.1 x 170 = 50 Leys 110) 4 de ear ② substitute values of y and 2 in 0-12 +0.1x110 + 0-2x170 550 . :-2 = 50) for the second supply possibility the production schedule should be 50000 artillary shells (A) 110000 band grenades (H) and 170000 bullets (8).