The company can start making a new semiautomatic gearbox that needs 4, 4, 1 and 1 hour respectively in each manufacturing stage, and gives a profit of £80 a unit. Should they make this new gearbox?

Amalgamated Engineering makes two kinds of gearbox – manual and automatic. There are four stages in the production of these, with details of times needed
and weekly availabilities given below. The company makes a profit of £64 on each manual gearbox sold and £100 on each automatic gearbox.

Stage in

manufacture

Time needed

(hours per unit)

Time available

(hours per week)

Manual

Automatic

Foundry

3

5

7,500

Machine shop

5

4

10,000

Assembly

2

1

3,500

Testing

1

1

2,000

(a) Find an optimal solution to the problem.

(b) The company can start making a new semiautomatic gearbox that needs 4, 4, 1 and 1 hour respectively in each manufacturing stage, and gives a profit of
£80 a unit. Should they make this new gearbox?

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