Question

company X manufactures four different types of toys for kids including cars, bikes

Answer 1

Answer:

A company manufactures two types of toys A and B. A toy of type A requires 5 minutes for cutting and 10 minutes for assembling. A toy of type B requires 8 minutes for cutting and 8 minutes for assembling. There are 3 hours available for cutting and 4 hours available for assembling the toy in a day. The profit is Rs.50 each on a toy of type A and Rs.60 each on a toy of type B. How many toys of each type should the company manufacture in a day to maximize the profit? Use linear programming to find the solution

Explanation:

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).

solution