Ms harris has a taco stand. she has found that her daily costs are approximated by the following equation:

c(x)=x^2-40x+610

c= the cost in dollars to sell 'x' units of tacos.

a. find the number of units of tacos she must sell to minimise her cost.

b. find the minimum cost.

show full working out

this is calculus

a. find the number of units of tacos she must sell to minimise her cost.
to find a minimum we need to find the function derivative and make it equal to zero:
dc/dx = 2x - 40 = 0
2x = 40
x = 20
therefore to minimize the cost, she needs to sell 20 units of tacos

b. find the minimum cost.
that can be done by substituting the previous result, 20 tacos, in the original equation:
C(x) = x^2 - 40x + 610
C(20) = (20)^2 - 40(20) + 610
= 400 - 800 + 610
= 210
the minimum cost will be 210 dollars