Problema Solution
A pizza shop makes $1.50 on each small pizza and $2.15 on each large pizza. On a typical friday, it sells between 70 and 90 small pizzas and between 100 and 140 large pizzas. The shop can make no more than 210 pizzas in a day. How many of each size pizza must be sold in order to maximize profit?
Answer provided by our tutors
let
x = the number of small pizzas sold
y = the number of big pizzas sold
it sells between 70 and 90 small pizzas
70 <= x <= 90
and between 100 and 140 large pizzas
100 <= y <= 140
the shop can make no more than 210 pizzas in a day
x + y <= 210
the profit is determined by
F(x , y) = 1.50x + 2.15y
lets draw the graph of the system of inequalities
70 <= x
x <= 90
100 <= y
y <= 140
x + y <= 210
click here to see the graph
look at the graph and find the notice the corner points!
there are 4 corner points and we calculate F(x ,y) for each point to find the maximum value (the biggest value for F):
(70, 100)
F(70, 100) = 1.5*70 + 2.15*100 = $320
(90, 100)
F(90, 100) = 1.5*90 + 2.15*100 = $350
(90, 120)
F(90, 120) = 1.5*90 + 2.15*120 = $393
(70, 140)
F(70, 140) = 1.5*70 + 2.15*140 = $406
to maximize the profit the company should sell 70 small pizzas and 140 big pizzas.