A small electronics company builds special large monitors for use in newspaper l
ID: 3034259 • Letter: A
Question
A small electronics company builds special large monitors for use in newspaper layout. Currently the company employees 5 workers who each make on average 30 monitors per day. Demand for these monitors is rising and the company wants to increase production. However, since the building space is small and tools are in limited supply, production per worker decreases by 2 monitors per day with every new employee hired. a) Write the equation for the total amount of monitors made. (use x for the number of new employees) b) What total number of workers allows the company to manufacture the largest number of monitors each day? c) How many monitors will be produced each day with this work force? d) If too many workers are hired there is so much confusion that no monitors are built in a day. How many workers makes this happen?Explanation / Answer
a). Let x be the number of new employees hired. Then, the average number of monitors produced per day per employee is 30 -2x so that the total number of monitors made per day is (5+x)(30-2x) = -2x2 +20x +150 = P (say).
b).If P is to be maximum, then dP/dx = 0 and d2P/dx2 should be negative. Here, dP/dx = -4x +20. Thus, if dp/dx = 0, then 4x = 20 so that x = 5. Also, d2P/dx2 = -4 which is negative. Hence, for a maximum production of monitors, 5 new employees should be hired.
c). If 5 new employees are hired, the total number of monitors made per day is (5+5)(30-2*5) =10*20 = 200.
d). If there is no production of monitors, then P = -2x2 +20x +150 = 0 or, 2x2 – 20x-150 = 0. On using the quadratic formula, we get x = [-(-20)±{(-20)2-4*2*(-150)]/2*2 = [20± (400+ 1200)]/4 = (20± 1600)/4 = ( 20+40)/4 = 15 ( as x cannot be negative). Thus, if 15 new employees are hired, no monitors will be produced.