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Question

A gold refinery refines both heavy gold and light gold that they use when creating jewellery. The table below shows the distribution of the gold that goes into different types of bracelets, earrings and necklaces.

(The table)

Bracelet Earrings Necklace

Heavy Gold 10% 17.5% 20%

Light Gold 20% 10% 16%

Note: Percentages do not add to 100 because there are other products not listed.

(Back to question)

The cost of heavy and light gold per unit is $45 and $38 respectively. Suppose the company needs to deliver at least 100,000 units of bracelets, 65,000 units of earrings and 250,000 units of necklaces.

a. Assuming x & y represent the units (100,000 units) of heavy and light gold bought by the refinery, write down a system of inequalities that describes the refinery’s distribution requirements.

Answer 1

Let's rewrite this table in terms of units.

The number of Heavy Gold units is x. That means the number of heavy gold bracelet units is .1x, earrings is .175x, and necklaces is .2x. Same for Light Gold where the number of units is y. That means the number of light gold bracelet units is .2y, earrings is .15y, and necklaces is .16y.

Bracelet Earrings Necklace

Heavy Gold .1x .175x .2x

Light Gold .2y .1y .16y

Now you can see the total bracelet units are .1x + .2y, total earrings units are .175 + .1y, and total necklace units are .2x + .16y.

You have the requirements for the total number of units in each category and can write out the inequalities now