Reference no: EM1390007
A small luxury watch manufacturing company makes two types of luxury watches, (1) Astro and (2) Cosmos. There are two production lines, one for each set, and there are two departments, both of which are used in the production of each watch. The capacity for the Astro line is 70 watched per day. The capacity for the Cosmos line is 50 watched per day. In department A, the chasses for both type watches are made. In this department, the Astro watch requires 1 hour of labor and the Cosmos chassis requires 2 hours of labor. Presently department A has a maximum capacity of 120 hours of labor. Department B is for the assembling work. In department B, the Astro watch requires 1 hour of assembling and a Cosmos watch requires 1 hour of assembling. Presently, department B has a maximum capacity of 90 labor hours per day. The profit margin for the Astro type watch is $200. The profit margin for the Cosmos type watch is $100.
PROBLEM FORMULATION:
The company makes two types of watches: Astro and Cosmos. We do not know how many units of each watch to make in order to maximize daily profits.
DECISION VARIABLES: Let XA = units of Astro watches to be produced per day
Let XC = units of Cosmos watches to be produced per day
OBJECTIVE FUNCTION: Company objective is to maximize profits
MAX P = 200XA + 100XB
Constraints: LINE CAPACITIES XA ? 70 Astro line
XC ? 50 Cosmos line
Constraints: LABOR CAPACITIES 1XA + 2XC ? 120 Dept. A
1XA + 1XC ? 90 Dept. B
Non-negativity XA, XC all ? 0
The entire LP problem is:
MAX P = 200XA + 100XB
S.T. XA ? 70
XC ? 50
1XA + 2XC ? 120
1XA + 1XC ? 90
XA, XC all ? 0
This Linear Program was solved by computer software
Questions:
(B) How much capacity of the Astro Line is used and how much is left over?
ANSWERS
(C) How much capacity of the Cosmos Line is used up and how much is left over?
ANSWERS
(D) How much capacity of labor in dept. A is used up and how much is left over?
ANSWERS
(E) How much capacity of labor in dept. B is used up and how much is left over?
ANSWERS
(F) Presently the capacity of ASTRO line is 70 watches per day. Suppose you wanted to increase the production line capacity for the ASTRO line by one unit, what maximum price should you pay for that increment?
ANSWER
(G) Presently the capacity of COSMOS line is 50 watches per day. Suppose you wanted to increase the production line capacity for the COSMOS line by one unit, what maximum price should you pay for that increment?
ANSWER
(H) Presently the capacity of labor hours in dept A is 120 hours per day. Suppose you want to increase that capacity by one hour, what maximum price should you pay for that increment?
ANSWER
(I) In the present optimal solution, of the two production lines, ASTRO and COSMOS, how many are in production (active)?
ANSWER
(J)Suppose the profit margin of the ASTRO watch drops to $90, what will happen to the production lines? (assume all other things stay the same)
ANSWER
(K) Suppose the profit margin of the ASTRO watch drops to $120, what will happen to the production lines? (assume all other things stay the same)
ANSWER
(L) Suppose the profit margin of the COSMOS watch increases to $120, what will happen to the production lines? (assume all other things stay the same)
ANSWER
(M) Suppose the profit margin of the COSMOS watch increases to $250, what will happen to the production lines? (assume all other things stay the same)
ANSWER
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