# math

A company is planning to purchase and store two items, gadgets and widgets. Each gadget costs \$2.00 and occupies 2 square meters of floor space; each widget costs \$3.00 and occupies 1 square meter of floor space. \$1,200 is available for purchasing these items and 800 square meters of floor space is available to store them. Each gadget contributes \$3.00 to profit and each widget contributes \$2.00 to profit.
Identify all constraints.
Identify all applicable corner points of the feasibility region.
What combination of gadgets and widgets produces maximum profit?

1. 👍
2. 👎
3. 👁
1. contraints
2 g + 3 w < 1200
2 g + w < 800
objective
p = 3 g + 2 w

corners (g,w)
(0,0)
if g = 0
w = 400 or 800, use 400 (0,400)
(0,400)
if w = 0
g = 600 or 400, use 400 (400,0)
intersection
2 g + 3 w = 1200
2 g + w = 800
------------------
2 w = 400
w = 200
g = 300 so (300,200)
-------------------------------
look at p
at (0,0) is 0
at (0,400) is 800
at (400,0) is 1200
at (300,200) is 3*300+2*200 = 1300
max profit of 1300 at (300,200)

1. 👍
2. 👎

## Similar Questions

1. ### Math

If a large factory sells its new gadgets for \$5 each it can sell 1050 per month and if it sells the same gadgets for \$9 it will sell 900 per month. Assuming the relationship between price and sales is linear predict the monthly

2. ### math

The MAthematical model C=500x+80,000 represents the cost in dollars a company has in manufacturing x items during a month. How many items were produced if costs reached \$250,000? I'm so stumped I don't even know where to start.

3. ### Math

In a shipment of 850 widgets, 32 are found to be defective. At this rate, how many defective widgets could be expected in 22,000 widgets? Round to the nearest whole number.

4. ### math

a custom printing store is planning on adding painters caps to its product line. For the first year the fixed costs for setting up production are \$15,000 the variable costs for producing a dozen caps are \$8 the revenue on each

1. ### Barber Scotia

your planning to buy a new computer monitor and printer for your office. you received the following prices: Store 1; Computer 2500 monitor 595 printer 398 Store 2 computer 2350 monitor 435 printer 349 find the total package price

2. ### system design

draw a use case diagram for the following situation Stillwater Antiques buys and sells one-of-a-kind antiques of all kinds. Each item is uniquely identified by an item number and is also characterized by a description, asking

3. ### economics

Suppose the price of widgets falls from \$7 to \$5 and consumption of widgets rises from 15 widgets a month to 25 widgets. Calculate your price elasticity of demand of widgets. What can you say about your price elasticity of demand

4. ### analazye profit functions

For a certain company, the cost function for producing x items is C(x)=40x+150 and the revenue function for selling x items is R(x)=−0.5(x−80)2+3,200. The maximum capacity of the company is 100 items. The profit function P(x)

1. ### math

The amount of revenue a company makes per day by selling x items is given by the function f(x) = 14x - 0.2x2. How many items should be sold if the company wants to maximize their profit?

2. ### math

a store charges \$28 for a sweater.this price is 40% more than the amount it costs the store.during a sale, store employees can purchase it at 30% off the stores cost. how much will it cost an employee to buy the sweater?

3. ### MATHEMATICS

Write a pseudocode that will accept items bought by a customer and place them in the appropriate class based on amounts calculated for the bill. Discounts are applied as follows: Silver – 1% Gold – 5% Platinum – 10% Tax on

4. ### algebra

You are an entrepreneur and selling handmade kites. Your company Kites-R-Fun has been contacted by a customer in Alaska who wants to purchase several of your best-selling kites and wants you to ship them to her. You have already