Question

A company produces two models of products, SUPER and ULTRA. Each SUPER model generates a profit...

  1. A company produces two models of products, SUPER and ULTRA. Each SUPER model generates a profit of $8, and each ULTRA model generates a profit of $5. The table below shows how many minutes are required to produce each model on two different machines with maximum available time. How many products of each model must be produced to maximize profit? How much is the maximum profit?

SUPER

ULTRA

Time Available

Machine 1

3 minutes

2 minutes

360 minutes

Machine 2

2 minutes

1 minute

200 minutes

* Let x be the number of SUPER products and y be the number of ULTRA products.

  1. Write a system of linear inequalities using all the constraints.

  1. Write an objective function (P).

  1. Graph the inequalities and shade the feasible region. Find and list all corners of the feasible region. Be sure to label your scales on each axis.
  1. Evaluate the objective function at each corner and state your final answer in a complete sentence.
Math   Calculus   
0 0
Add a commentTranscribed image text
Next >

Homework Answers

Answer #1

The system of linear inequalities are

The objective is to maximize profit. So

The graph is as follows

The corners of the feasible region are B(0,180), A(40,120) and C(100,0).

Evaluating the objective function in the corners:

Thus 40 units of SUPER model and 120 units of the ULTRA model must be produced to maximize profit. The maximum profit is $920.

0 0
Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Log In

Sign Up

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
A company manufactures two products, A and B, on two machines, I and II. The profit...
A company manufactures two products, A and B, on two machines, I and II. The profit is $3 on each unit of product A and $4 on each unit of product B. To manufacture a unit of product A requires 6 minutes on machine I and 5 minutes on machine II. To manufacture a unit of product B requires 9 minutes on machine I and 4 minutes on machine II. There are 300 minutes of machine time available on machine...
Company A makes 2 models of radios. Model 1 provides a profit of $54 for each...
Company A makes 2 models of radios. Model 1 provides a profit of $54 for each unit, while model 2 provides a profit of $72. Two units materials will be required to make one model 1 Radio, while model 2 needs four units. In addition a model 1 takes 4 hours of the time to produce and model 2 takes 5 hours. If 100 units of raw materials and 140 hours of production times are available, how many of each...
A company manufactures two products: large fans and medium fans. Each large fan requires 3 hours...
A company manufactures two products: large fans and medium fans. Each large fan requires 3 hours of wiring and 2 hours of drilling. Each medium fan requires 2 hours of wiring and 1 hour of drilling. There are 480 hours of wiring time available and 280 hours of drilling time available. Each large fan yields a profit of $25. Each medium fan yields a profit of $18. The company wants to manufacture at least 20 large fans. The objective is...
A company manufactures two products: large fans and medium fans. Each large fan requires 3 hours...
A company manufactures two products: large fans and medium fans. Each large fan requires 3 hours of wiring and 2 hours of drilling. Each medium fan requires 2 hours of wiring and 1 hour of drilling. There are 480 hours of wiring time available and 280 hours of drilling time available. Each large fan yields a profit of $25. Each medium fan yields a profit of $18. The company wants to manufacture at least 20 large fans. The objective is...
A manufacturer wants to maximize the profit of two products. Product I yields a profit of...
A manufacturer wants to maximize the profit of two products. Product I yields a profit of $ 1.50 per unit, and product II yields a profit of $2.00 per unit. Market tests and available resources have indicated the following constraints: • The combined production level should not exceed 1200 units per month. • The demand for product II is no more than half the demand for product I. • The production level of product I is less than or equal...
Cully Furniture buys two products for resale: big shelves (B)and medium shelves (M). Each big shelf...
Cully Furniture buys two products for resale: big shelves (B)and medium shelves (M). Each big shelf costs $500 and requires 100 cubic feet of storage space, and each medium shelf costs $300 and requires 90 cubic feet of storage space. The company has $75,000 to invest in shelves this week, and the warehouse has 18,000 cubic feet available for storage. Profit for each big shelf is $300 and for each medium shelf is $150. SHOW WORK. A) Write the Linear...
A manufacturer produces two products, P and Q, which when sold earn contributions of  £600 and  £400 per...
A manufacturer produces two products, P and Q, which when sold earn contributions of  £600 and  £400 per unit respectively.  The manufacturer of each product requires time on a lathe and a polishing machine. Each unit of P requires 2 hours on the lathe and 1 hour on the polishing machine, while Q requires 1 hour on each machine.  Each day, 10 hours are available on the lathe and 7 hours on the polishing machine.  Determine the number of units of P and Q that...
Professional Printers, Inc.make two models of commercial printers (FlowPrint and TypeIt). Manufacturing time requirements for each...
Professional Printers, Inc.make two models of commercial printers (FlowPrint and TypeIt). Manufacturing time requirements for each printer is given below. SHOW ALL WORK FlowPrint Model TypeIt Model Hours Available Plastic 2 4 38 Ink Assembly 2 5 44 Molding Time 5 3 34 ​The profit for the FlowPrint model is $1000 per printer and the profit for the TypeIt model is $2000 per printer. Formulate the linear programming problem only. Be sure to define decision variables, provide objective function, and...
A television manufacturer makes rear-projection and plasma televisions. The profit per unit is $125 for the...
A television manufacturer makes rear-projection and plasma televisions. The profit per unit is $125 for the rear-projection televisions and $200 for the plasma televisions. a. Let ?? = the number of rear-projection televisions manufactured in a month and ?? = the number of plasma televisions manufactured in a month. Write the objective function that models the total monthly profit. b. The manufacturer is bound by the following constraints: ? Equipment in the factory allows for making at most 450 rear-projection...
A television manufacturer makes rear-projection and plasma televisions. The profit per unit is $125 for the...
A television manufacturer makes rear-projection and plasma televisions. The profit per unit is $125 for the rear-projection televisions and $200 for the plasma televisions. a. Let ?? = the number of rear-projection televisions manufactured in a month and ?? = the number of plasma televisions manufactured in a month. Write the objective function that models the total monthly profit. b. The manufacturer is bound by the following constraints: ? Equipment in the factory allows for making at most 450 rear-projection...
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT