Question

Company X manufactures four different types of toys for kids including cars, bikes, plane and
ship. The gross margin, production, and profit are listed below for each items are shown below
Car
Plane
Bike
1.2
Ship
1.2
0.3
0.75
1
2.5
15
2
Product
Gross margin/unit
Minutes/unit
Gross margin/minute
Maximum production
Profit
0.30
0.52
0.50
280000
112000
18667
0.60
140000
168000
84000
145600
14000
Let the production capacity of the machine used for production is 4500 hours per year. What would
be the effect on optimal solution and profit, if the gross margin for plane would become 0.85?
(A) Optimal solution and profit both increase
B) Optimal solution and profit both remain unchanged
(C) Profit would increase, but change in optimal solution cannot be determined
D) Optimal solution will remain same, but profit will increase​

Answer 1

Answer:

Toy A  Toy B  Time in a day

Cutting time 5 min 8 min 180 min

Assembling time 10 min 8 min 240 min

Profit 50 60

Assumed quantity x y

Profit function z=50x+60y

5x+8y=180

A B

x         0 36

y 22.5    0

x≥0,y≥0

5x+8y≤180

10x+8y≤240 or 5x+4y≤120

5x+4y=120

 C      D

x  0 24

y      30 0

Corner point z=50x+60y

At O(0,0)                 0

At D(24,0) 1200

At E(12,15) 1500

At A(0,22.5) 1350

Hence the maximum profit is Rs.1500 at E(12,15).

Explanation: