Question 1141850
cost function for machine 1 is 19000 + 13 * x.


cost function for machine 2 is 15000 + 19 * x.


revenue function is 60 * x


x represents the number of units produced and sold.


when 450 units are sold ........,


revenue is 60 * 450 = 27,000
cost using machine 1 is 19000 + 13 * 450 = 24,850
cost using machine 2 is 15000 + 19 * 450 = 23,550


profit using machine 1 is 27,000 - 24,850 = 2,150
profit using machine 2 is 27,000 - 23,550 = 3,450


profit using machine 2 is more than profit using machine 1.


when 550 units are sold .........,


revenue is 60 * 550 = 33,000
cost using machine 1 is 19000 + 13 * 550 = 26,150
cost using machine 2 is 15000 + 19 * 550 = 25,450


profit using machine 1 is 33,000 - 26,150 = 6,850
profit using machine 2 is 33,000 - 25,450 = 7,550


profit using machine 2 is more than profit using machine 1.


when 650 units are sold .............,


revenue is 60 * 650 = 39,000
cost using machine 1 is 19000 + 13 * 650 = 27,450
cost using machine 2 is 15000 + 19 * 650 = 27,350 


profit using machine 1 is 39,000 - 27,450 = 11,550
profit using machine 2 is 39,000 - 27,350 = 11,650


profit using machine 2 is more than profit using machine 1.


profit is equal to revenue minus cost.
if the revenue is the same regardless of which machine is used, then the greater profit is given to the machine that uses the least cost.


the break even point where the cost for using machine 1 versus using machine 2 is found by making their cost functions equal to each other.


you get 19000 + 13 * x = 15000 + 19 * x
subtract 15000 from both sides of this equation and subtract 13 * x from both sides of this equation to get 19000 - 15000 = 19 * x - 13 * x.
combine like terms to get 4000 = 6 * x
solve for x to get x = 666.67 units.
with that number of units, the cost of using machine 1 is the same as the cost of using machine 2.
when the number of units produced and sold are greater than that, machine 1 provides more profit.


for example, when 750 units are produced .........,
revenue is 60 * 750 = 45,000
cost for machine 1 is 19000 + 13 * 750 = 28,750
cost for machine 2 is 15000 + 19 * 750 = 29,250
profit for machine 1 is 45,000 - 28,750 = 16,250
profit for machine 2 is 45,000 - 29,250 = 15,750


profit using machine 1 is more than profit using machine 2.


the following graph shows revenue and cost at 450, 550, 650, and 750 units.


graph of revenue is green.
graph of cost for machine 1 is red.
graph of cost for machine 2 is blue


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