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 are