The first step, and the key to success, is picking out the question. Will profit increase? We need to determine the profit for each of the two choices to find out which is greater. The formula for profit P is given by

P  =  RC

where R represents the total revenue, and C represents the total cost.

From here the problem has been broken up into four smaller problems. Each of these problems can be solved by writing down what we know.

What is the monthly cost for 8-hour production?

C8  =  $250,000

What is the monthly revenue for 8-hour production? The monthly revenue depends on three factors given in the problem. The production rate r = 150 wagon/hr, the amount of production time during the month t8 = (21 days)(8 hr/day) = 168 hr, and the price per wagon p8 = $15/wagon.

R8  =  r t8 p8  =  (150 wagon/hr) (168 hr) ($15/wagon)  =  $(150 · 168 · 15)  =  $378,000

Note that we represented the production rate with a simple symbol r, because the production rate (in wagons per hour) doesn't depend on the level of production. On the other hand, we used subscripted symbols R8, C8, t8, and p8 because these all depend on the level of production

What is the total monthly cost if production is increased by 3,000 wagons per month? To answer this, we need to determine how many additional hours of production are needed, since that's what determines our added cost. We need to produce 3,000 additional wagons at a rate of 150 wagon/hr. This will take an addtional time

t+  =  (3000 wagon)/(150 wagon/hr)  =  (3000/150) hr  =  20 hr

Knowing the additional production time, we can determine the additional cost

C+  =  ($1,750/hr) t+  =  ($1,750/hr)(20 hr)  =  $(1,750 · 20)  =  $35,000

The total cost if production is increased by 3,000 wagons is

COT  =  C8 + C+  =  $250,000 + $35,000 = $285,000

What is the total monthly revenue if production is increased by 3,000 units per month? Let's first find the total production time

tOT  =  t8 + t+  =  168 hr + 20 hr  =  188 hr

Then we can use our revenue formula to find

ROT  =  r tOT pOT  =  (150 wagon/hr) (188 hr) ($14/wagon)  =  $(150 · 188 · 14)  =  $394,800

Now we can compare the profit in each case:

P8  =  R8C8  =  $378,000 – $250,000  =  $128,000
POT  =  ROTCOT  =  $394,000 – $285,000  =  $109,800

Now we can see that it does not make sense to lower the price and increase production, since profit would decrease.