Amanufacturing company receives orders for engines from two assembly plants. plant i needs at least 45 engines, and plant ii needs at least 32 engines. the company can send at most 120 engines to these assembly plants. it costs $30 per engine to ship to plant i and $40 per engine to ship to plant ii. plant i gives the manufacturing company $20 in rebates toward its products for each engine they buy, while plant ii gives similar $10 rebates. the manufacturer estimates that they need at least $1500 in rebates to cover products they plan to buy from the two plants. how many engines should be shipped to each plant to minimize shipping costs? what is the minimum cost?

answer: y = 3/2 x - 3

y = 1/8 x - 3/4 that would be your correct option

step-by-step explanation: w

wait this depends wether emily and zach how they are thinking.

yes they are the same.

a) 40 more; b) old factory:   10%, new factory:   16%; c) week 4

explanation:

a) at week 0, we see in the graph that the new factory produces 190 specialty items.  

using the function, substituting 0 in for w,

this is a difference of 230-190 = 40.

b) the function for the old factory is written in the form f(x) = a(1+r)ˣ, where a is the original amount, x is the amount of time and r is the growth rate.   the equation for the old factory is ; 230 is in place of a and is the original amount; w is the amount of time; which means 1+r = 1.1.   this means that r must be 0.1 or 10%.

for the new factory, we find the percent of increase to find the growth rate; the formula for this is

between the first two points, the amount of change is 220-190 = 30; this gives us

30/190 = 0.158 ≈ 0.16 = 16%

c) at week 0, the old factory has 230 while the new factory has 190.

at week 1, the old factory has 230(1.1) = 253 while the new factory has 220.

at week 2, the old factory has 230(1.1²) = 278.3 while the new factory has 252.

at week 3, the old factory has 230(1.1³) = 306.13 while the new factory has 290.

at week 4, the old factory has 230(1.1⁴) = 336.743 while the new factory has 337.   this is the first week that the new factory surpasses the old.