Question

A small company manufactures both large and small grandfather clocks. The company can make no more than 8 clocks a day. They want to build no more than 5 large clocks and no more than 6 small clocks per day. The company makes a profit of $100 on each large clock and $75 on each small clock. The company wishes to maximize its profit.

What is the objective function for this situation?


8 ≥ x + y


8 ≥ 100x + 75y


P ≥ 100x + 75y


P = 100x + 75y

Answer 1

P = 100x + 75y

Explanation:

The objective is profit, so the objective function is the function that defines profit:

P = 100x + 75y

where x is the number of large clocks made and y is the number of small clocks made per day.

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Comment on other choices

Inequalities are generally associated with constraints on the manufacturing. Here, those would be ...

• 0 ≤ x ≤ 5 no more than 5 large clocks
• 0 ≤ y ≤ 6 no more than 6 small clocks
• x + y ≤ 8 no more than 8 clocks total

The variables are constrained to be non-negative, because we cannot build a negative number of clocks.

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To maximize profit in this situation, the maximum possible number of large clocks should be produced, since they are the most profitable. Then the remaining capacity should be used to produce as many small clocks as possible: 5 large clocks and 3 small clocks for a profit of $725 per day.