Linear Programming word problem

Question

linear programming problem 2

Gorilla Joe Costumes runs a Costume company that supplies custom gorilla suits for sale to customers. The company has two sizes, the Gorilla and the Chimp Gorilla. The Giant suit takes 4 hours to make and the Chimp suit takes 2 hours to make. The company has only up to 32 hours available a week to produce the suit. The company can display and sell the suit on Friday each week and has room for only up to 10 suits in its showroom.

The company makes a profit of $260 on the Giant Gorilla costume and $230 on the chimp Gorilla costume.

Assuming that all the suit are sold on Friday, How many Chimp and how many Giant suits should the company make to maximize profit.

Identify your variable.

create your functions formula with these variables.

Write your system of inequalities that make up your constraints.

Graph your system of inequalities.

Show your polygonal feasibility solutions set.

Identify the corner or vertex point of your polygonal set.

use these points in your functions formula to find the maximum value.

give your answer completely in sentences.

Please explain step by step and graphing as well.

Answer 1

Giant takes 4 hours, bigger things take bigger time, so to speak, Gorillas maybe twice the size of Chimps

while 4 hrs/wk = twice 2 hr/wk

260 hrs is far from twice 230 hrs 260<<2(230)

so 1st guess is do all chimps, 16 c, 0 G

chimps beat Gorillas, (ignoring their usual likely encounters)

Chimp takes 2 hours to make

32 hours max for both combined, which means 16 max chimps, 8 max Giants, per week

or

4G+2c = 32

or

2G + c = 16

c= 16-2G

graph with c on x axis, G on y axis

a straight line boundary with x intercept = 16, y intercept=8

room only for 10 in their showroom each week

this is seemingly significant information, but seems far more irrelevant, without more information maybe on advertizing costs

$260 profit on each G, $230 on each chimp

do all Gorillas and P =8(260)= $2,080 Profit

do all on chimps and P=16(230) = $3,680 Profit

16x230 = $3,630 max profit, with all chimps, zero Gorillas

chimps beat Gorillas almost 2 to 1,

they name sports teams after animals, maybe it's time for the New York (SF lately) Giant Gorillas to lose to the Brooklyn (now LA) dodger chimps. Eagles just lost to the frogs in the Superbowl. It happens. eagles/frogs roughly = the gorilla/chimps ratio. Give or take a little DNA

graph the constraint, it's a line with slope =-1/2

graph the indifference curves, the max profit curve (line) intersects at (16,0) =(c,G)

production possibilities vertices are (0,0), (8,0), (16,0). It's a triangle

if the question makes sense, or if I understand it The Friday thing is confusiing

or irrelevant.

You could get a headache thinking about it.