A manufacturing plant produces computer mice, keyboards, and video game consoles. The sales price, per-unit cost, per-unit labor usage, per-unit machine-time usage, and monthly demand are given in the following table (also in worksheet): Each month, a total of 13,000 labor hours and 3,000 hours of machine time are available. How much of each product will maximize profit? Find and record the optimal amount of each product What is the maximized amount of profit?

A manufacturing plant produces computer mice, keyboards, and video game consoles. The sales price, per-unit cost, per-unit labor usage, per-unit machine-time usage, and monthly demand are given in the following table (also in worksheet): Each month, a total of 13,000 labor hours and 3,000 hours of machine time are available. How much of each product will maximize profit? Find and record the optimal amount of each product What is the maximized amount of profit?

College Algebra

10th Edition

ISBN:9781337282291

Author:Ron Larson

Publisher:Ron Larson

Chapter6: Systems Of Equations And Inequalities

Section: Chapter Questions

Problem 21T: A manufacturer produces two models of television stands. The table at the left shows the times (in...

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A manufacturer produces two models of television stands. The table at the left shows the times (in hours) required for assembling, staining, and packaging the two models. The total times available for assembling, staining, and packaging are 3750 hours, 8950 hours, and 2650 hours, respectively. The profits per unit are $30 for model I and $40 for model II. What is the optimal inventory level for each model? What is the optimal profit?
Inventories An electronics store manager stocks from 20 to 30 IBM-compatible computers and from 30 to 50 Apple computers. There is room in the store to stock up to 60 computers. The manager receives a commission of 50 on the sale of each IBM-compatible computer and 40 on the sale of each Apple computer. If the manager can sell all of the computers, how many should she stock to maximize her commissions? Find the maximum commission. Inventory IBM Apple Minimum 20 30 Maximum 30 50 Commission 50 40
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.
Making furniture Two woodworkers, Chase and Devin, get 100 for making a table and 80 for making a chair. On average, Chase must work 3 hours and Devin 2 hours to make a chair. Chase must work 2 hours and Devin 6 hours to make a table. If neither wishes to work more than 42 hours per week, how many tables and how many chairs should they make each week to maximize their income? Find the maximum income. Table Chair Time Available Devins Time hr 6 2 42 Chases Time hr 2 3 42 Income 100 80
In Example 3, if the accountant earns a profit of 100 on each individual return and a profit of 175 on each business return, find the maximum profit. An accountant prepares tax returns for individuals and for small businesses. On average, each individual return requires 3 hours of her time and 1 hour of computer time. Each business return requires 4 hours of her time and 2 hours of computer time. Because of other business considerations, her time is limited to 240 hours, and the computer time is limited to 100 hours. If she earns a profit of 80 on each individual return and a profit of 150 on each business return, how many returns of each type should she prepare to maximize her profit?

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	Mice	Keyboards	Console
Sale Price	10	20	16
Cost to Produce	2	9	7
Labor usage/unit (hours)	0.2	0.3	0.24
Machine time/unit (hours)	0.04	0.055	0.04
Monthly demand	15000	29000	11000