A chemical manufacturer produces two products, chemical X and chemical Y. Each p

Question

A chemical manufacturer produces two products, chemical X and chemical Y. Each product is manufactured by a two-step process that involves blending and mixing in machine A and packaging on machine B. Chemical X provides a $55/unit contribution to profit, while Chemical Y provides a $60 contribution to profit. The processing times for the two products on the mixing machine (A) and the packaging machine (B) are as follows:

Product

Machine A

Machine B

(hours)

(hours)

Chemical X

3

3

Chemical Y

5

2

For the upcoming two-week period, machine A has available 90 hours and machine B has available 60 hours of processing time. Forecasts of the markets indicate that the manufacturer can expect to sell a maximum of 16 units of chemical X and 18 units of chemical Y.

The algebraic expression for the constraint on machine B (when exhausting all available machine hours) is

2x + 3y = 60

3x + 2y = 60

3x+2y = 90

x = 60

Product

Machine A

Machine B

(hours)

(hours)

Chemical X

3

3

Chemical Y

5

2

Explanation / Answer

Machine B is available for 60 hours

It takes 3 hours for packaging of Chemical X and 2 hours for packaging of Chemical Y

If the time consumed for Chemical X be x and for Chmical Y be y

Then the required equation comes out to be

3x + 2y = 60

Option B

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