I need a solution to a certain math word problem I just cannot solve?

Question

For some reason the words and numbers get me confuse and I don't know exactly when to multiply, subtract, divide etc.

Math problem: The Champion Lumber Company converts logs into lumber or plywood. In a given week, the total production cannot exceed 800 units, of which 200 units of lumber and 300 units of plywood are required by regular customers. The profit on a unit of lumber is $20.00 and the profit on a unit of plywood is $30.00. Find the number of units each of lumber and plywood that should be produced to maximize profit. What is the maximum profit?

Can someone please help me?

Answer 1

let L = number of lumbar units
P = number of plywood units

here's what you know

L=>200
P =>300

20 x L + 30 x P = profit

L+P <=800


since the profit on P is > profit on L, your maximum profit will occur when the amount of P is maximized and the amount of L is minimized for a fixed amount of production.

so, max occurs when L is 200 and P is 600

in which case profit is 20 x 200 + 30 x 600 = 4000+18000 = 22000

Answer 2

Let L denote the number of units of lumber produced and P denote the units of plywood. We know that L + P <= 800, L >= 200, P >= 300, and the total gain is 20L + 30 P.

Since we want to maximize the gain, we should take L + P = 800, or L = 800 - P. With this value for L in the expression 20L + 30P, we get 20*(800 - P) + 30 P = 16 000 + 10P is the gain. To maximize gain we shoulp take the largest possible value for P; since L is at least 200, the largest P can be is 600. Therefore, max profit is 16 000 + 10*600 =22 000.

Answer 3

They make more profit on plywood, and they don't need more than 200 units of lumber. So, what I would do is:

800-(200+300)=300

That would be 600 units of plywood @ $30 profit each
and 200 units of lumber @ $20 profit each

(600X30) + (200X20) = maximum profit
18000+ 4000 = $22,000 maximum profit

Answer 4

The text tells you that you must produce at least 200 lumber and 300 plywood, which is 500 units committed.

You therefore have 800-500=300 units capacity left.
Since plywood pays better than lumber, make all 300 units of plywood, representing 600 units in all.

Profix(max) = 200*$20 + 600*$30
Profix(max) = 4,000 + 18,000 = $22,000

Answer 5

the total maximum is 800 units in total each week

and each week -
200 units of lumber are made
300 units of plywood

profit per unit of items
lumer per unit = $20
plywood per unit =$30

current profit per week is worked out -

lumber $20 * 200units = $4000
plywood $30 * 300units = $9000
total per week = $13,000

then you now need to work out different amount of units like abaove to find the maximum amount that you ca make

1. lumber $20*400units = $8,000
plywood $30*400units=$12,000
total = $20,000

2. lumber $20*200units=$4000
plywood $30*600units=$18,000
total = $22,000

3. lumber $20*100units=$2000
plywood $30*700units=$21,000
total= $23,000

so option 3 would be better and more profitable for the company.

and the difference in profit you would work out like this

$23,000 - $13,000 = $10,000 more then they more earning before

Answer 6

I think you do
200*20=4000
300*30=9000
Then add them up =13000
Your allowed 800 units and 200+300 is only 500, and plywood make more money so add 300 more plywood.
300*30=9000
13000+9000= 22000
$22,000 is the maximum profit. Or at least I believe so, I'm not positive though.

Answer 7

i wont resolve all yet whilst i answer one u can take the cue.... a million.) enable jane's age be x therefor sara is x+5 and darsi is 2x 2x+x+5+x=sixty 5 4x + 5 = sixty 5 4x = 60 x = 15 as a result Jane is 15 ....Darsi is 30 and Sara is 20