Amanufacturer produces a battery-powered calculator and a solar model. the battery-powered model requires 10 min of electronic assembly and the solar model 15 min. there are 450 min of assembly time available per day. both models require 8 min for packaging, and 280 min of packaging time are available per day. if the manufacturer wants to use all the available time, how many of each unit should be produced per day?

Oh the wrong answer got deleted so here I am :)

Set up a system of equations. Let's make battery B and solar S where B and S represent the number of units.
Step 1: The first two sentences talk about assembly.
For Battery, it would be 10B.
For Solar, it would be 15S.
If you add 10B and 15S, it would take about 450 min total:
10B+15S=450

Step 2: Now for the second equation. Both take 8 min, so 8B + 8S = 280 min.

Step 3: Solve for a variable. Let's do the second equation.
8B + 8S = 280               Subtracted 8B from both sides.
8S = 280 - 8B                Divided both sides by 8 to get S by itself.
S=  - B
S = 35 - B      Simplified, 280 divided by 8 = 35.

Now plug in S into the first equation.
10B + 15S = 450
10B + 15(35-B) = 450
10B + 525 - 15B = 450
-5B = -75
B=15

Then you can plug in 15 for either of the first two equations to get S.
10B+15S=450
10(15)+15S=450
S=20

So 15 battery powered units and 20 solar powered units.

The vertex of the quadratic function is (1.5, -.75)