A firm offers three different prices on its products, depending upon the quantity purchased. Since available resources are limited, thefirm would like to prepare an optimal production plan to maximize profits. Product 1 has the following profitability: $11 each for the first55 units, $10 each for units 56-110, and $9 for each unit over 110. Product 2's profitability is $19 each for the first 30 units, $18 each forunits 31-60, and $17 each for each unit over 60. The products each require 3 raw materials to produce (see table below for usagesand available quantities).Product 1 usage (poundsProduct 2 usage (poundsAvailable QuantityRaw Materialper unit)per unit)(pounds)A731,300BC141212151,5002,500Use separable programming to find the optimal production plan.(Leave no cells blank - be certain to enter "O" wherever required. Round the first two answers (units of Product 1 and 2) to thenearest whole number. Round the total profit answer to 2 decimal places and use unrounded unit quantities to compute it.)units of Product 1 andunits of Product 2.The total profit from this plan will be

I'll solve this step by step using separable programming to maximize profit while respecting…

Answered: A firm offers three different prices on…

College Algebra (MindTap Course List)

12th Edition

ISBN:9781305652231

Author:R. David Gustafson, Jeff Hughes

Publisher:R. David Gustafson, Jeff Hughes

Chapter6: Linear Systems

Section6.8: Linear Programming

Problem 5SC: If during the following year it is predicted that each comedy skit will generate 30 thousand and...

See similar textbooks

Question

A firm offers three different prices on its products, depending upon the quantity purchased. Since available resources are limited, the
firm would like to prepare an optimal production plan to maximize profits. Product 1 has the following profitability: $11 each for the first
55 units, $10 each for units 56-110, and $9 for each unit over 110. Product 2's profitability is $19 each for the first 30 units, $18 each for
units 31-60, and $17 each for each unit over 60. The products each require 3 raw materials to produce (see table below for usages
and available quantities).
Product 1 usage (pounds
Product 2 usage (pounds
Available Quantity
Raw Material
per unit)
per unit)
(pounds)
A
7
3
1,300
B
C
14
12
12
15
1,500
2,500
Use separable programming to find the optimal production plan.
(Leave no cells blank - be certain to enter "O" wherever required. Round the first two answers (units of Product 1 and 2) to the
nearest whole number. Round the total profit answer to 2 decimal places and use unrounded unit quantities to compute it.)
units of Product 1 and
units of Product 2.
The total profit from this plan will be

Expert Solution

Step by step

Solved in 2 steps

SEE SOLUTION Check out a sample Q&A here

Similar questions

If during the following year it is predicted that each comedy skit will generate 30 thousand and each musical number 20 thousand, find the maximum income for the year. A television program director must schedule comedy skits and musical numbers for prime-time variety shows. Each comedy skit requires 2 hours of rehearsal time, costs 3000, and brings in 20,000 from the shows sponsors. Each musical number requires 1 hour of rehearsal time, costs 6000, and generates 12,000. If 250 hours are available for rehearsal and 600,000 is budgeted for comedy and music, how many segments of each type should be produced to maximize income? Find the maximum income.
A company uses 5000 items per annum which has a price of $2 each. The ordering costs are $150 per order and holding costs are $1.50 per item per annum. The company is offered a 5% discount (discounted price is $1.90) for orders of 5000 and over. Order cost and holding cost remain at $150 per order and $1.50 respectively. Assuming that the company orders 5000 items per order, calculate the number of orders per annum, average stock, annual stock holding cost, annual order cost, annual inventory cost and the total annual cost of items and inventory.
A local consulting firm currently has 5 jobs that have to be completed by its contract employees. After analyzing the time that it would take each specific employee to complete each specific job, and, the wages each specific employee is paid per hour, it determined how much it would cost if specific employees were assigned to specific jobs. These costs were calculated to be: Cost ($) Job Employee 1 2 3 4 5 A 1,200 1,850 1,375 3,500 1,900 B 1,175 1,920 1,540 3,375 2,050 C 1,080 1,885 1,475 3,400 2,010 D 1,190 1,905 1,400 3,600 2,100 E 1,250 1,900 1,390 3,520 1,975 F 1,200 1,950 1,465 3,400 1,950 G 1,075 1,820 1,480 3,250 1,920 a. If each employee can only be assigned at most one job and each job requires only one employee, which employees should be assigned to…
Flint lab produces 4 high tech product types. Each of the products must be wired, drilled, assembled and checked for quality standard before being delivered to consumers. The time requirement and profit for each product are as follows. Product A: 0.5 hr for wiring, 3 hrs for drilling, 1 hr for assembling, and 0.5 hr for inspection. One product A can be sold for $10 per unit. Product B: 1.5 hr for wiring, 1 hrs for drilling, 3 hrs for assembling, and 1 hr for inspection. One product B can be sold for $13 per unit. Product C: 1.5 hr for wiring, 2 hrs for drilling, 3 hrs for assembling, and 0.5 hr for inspection. One product C can be sold for $16 per unit. Product D: 1 hr for wiring, 3 hrs for drilling, 2 hrs for assembling, and 0.5 hr for inspection. One product D can be sold for $12 per unit. The maximum capacity for wiring, drilling, assembly, and inspection are 1500 hrs; 2350 hrs; 2600 hrs; and 1200 hrs respectively. Flint lab requires that there will be at least 150 units of A, 100…
National Business Machines manufactures x model A portable printers and y model B portable printers. Each model A costs $100 to make, and each model B costs $150. The profits are $35 for each model A and $45 for each modelB portable printer. If the total number of portable printers demanded per month does not exceed 2500 and the company has earmarked no more than $600,000/month for manufacturing costs, how many units of each model should National make each month to maximize its monthly profit? 1) (х, у) What is the optimal profit? $
A company makes pancake mix and cake mix. Each pound of pancake mix uses 0.6 lb of flour and 0.1 lb of shortening. Each pound of cake mix uses 0.4 lb of flour, 0.1 lb of shortening, and 0.4 lb of sugar. Suppliers can deliver at most 6,000 lb of flour, at least 500 lb of shortening, and at most 1,200 lb of sugar. If the profit per pound is $0.45 for pancake mix and $0.35 for cake mix, how many pounds of each mix should be made to earn maximum profit? pancake mix 2000 Xlb lb cake mix 3000 What is the maximum profit (in $)? $3450 X
refer to image below.
1. A manufacturer produces two types of calculators, business calculators and scientific calculators. Each business calculator requires 3 circuit boards and 4 hours of assembly time while the scientific calculator requires 2 circuit boards and 1 hour of assembly time. The profit of each business calculator and scientific calculator are RM 12 and RM 20 respectively. The company produces its own circuit boards and the capacity is 60 perweek. Currently the company has 72 hours of assembly time per week. The demand for business calculator is at least 8 units per week. The company wishes to maximize the profit.a) Formulate the problem as a linear programming model.b) Solve the problem graphically. What is the maximum profit?
A company makes three types of candy and packages them in three assortments. Assortment I contains 4 sour, 4 lemon, and 12 lime candies, and sells for P94. Assortment II contains 12 sour, 4 lemon, and 4 lime candies, and sells for P76. Assortment III contains 8 sour, 8 lemon, and 8 lime candies, and sells for P110. Manufacturing costs per piece of candy are P2 for sour, P2.50 for lemon, and P3 for lime. They can make 5,200 sour, 3,800 lemon, and 6,000 lime candies weekly. How many boxes of each type should the company produce each week in order to maximize its profit? What is the maximum profit?
A beauty shop specializing in permanents has fixed costs of $1987.20 per month. The owner estimates that the cost for each permanent is $23.60, which covers labor, chemicals, and electricity. If her shop can give as many permanents as she wants at a price of $42 each, how many must be given each month to break even? O108 permanents O109 permanents O106 permanents O103 permanents O105 permanents

Recommended textbooks for you

College Algebra (MindTap Course List)

Algebra

ISBN:

9781305652231

Author:

R. David Gustafson, Jeff Hughes

Publisher:

Cengage Learning

Linear Algebra: A Modern Introduction

Algebra

ISBN:

9781285463247

Author:

David Poole

Publisher:

Cengage Learning

Algebra for College Students

Algebra

ISBN:

9781285195780

Author:

Jerome E. Kaufmann, Karen L. Schwitters

Publisher:

Cengage Learning

College Algebra (MindTap Course List)

Algebra

ISBN:

9781305652231

Author:

R. David Gustafson, Jeff Hughes

Publisher:

Cengage Learning

Linear Algebra: A Modern Introduction

Algebra

ISBN:

9781285463247

Author:

David Poole

Publisher:

Cengage Learning

Algebra for College Students

Algebra

ISBN:

9781285195780

Author:

Jerome E. Kaufmann, Karen L. Schwitters

Publisher:

Cengage Learning

SEE MORE TEXTBOOKS