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The production cost of widget A is $5 per unit and the
selling price is $8 per unit. The production cost of
widget B is $7 per unit and the selling price is $10 per
unit. The company can produce at most 1000 widgets
per day, and the demand for each type of widget is at
least 300 units per day. How many units of each type of
widget should the company produce to maximize its
profit?
a) 300 units of A and 700 units of B
b) 400 units of A and 600 units of B
c) 500 units of A and 500 units of B
d) 600 units of A and 400 units of B
Answer: b) 400 units of A and 600 units of B
Rationale: The profit function is P = 3A + 3B, where A
and B are the number of units of widget A and B,
respectively. The constraints are A + B ≤ 1000, A ≥
300, and B ≥ 300. Using the graphical method, we can
find the feasible region and the corner points. The
corner points are (300, 700), (400, 600), (700, 300), and
(1000, 0). Evaluating the profit function at each corner
point, we find that P is maximized when A = 400 and B
= 600, with a maximum profit of $3600.
2. A farmer has a rectangular field with a perimeter of
200 meters. He wants to divide the field into two plots
by building a fence parallel to one of the sides. What areÂÂ
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