A craftsman named William Barnes builds two kinds of birdhouses, one for wrens and a second for bluebirds. Each wren birdhouse takes 4 hours of labor and 4 units of lumber. Each bluebird house requires 2 hours of labor and 12 units of lumber. The craftsman has available 72 hours of labor and 120 units of lumber. Wren houses yield a profit of $ 10 each and bluebird houses yield a profit of $ 15 each. The aim of the objective function for William should be to ▼ Minimize Maximize the objective value.

Goods and services that can be used for the same purpose are and goods and services that are used together are

Following is a list of various costs incurred in producing replacement automobile parts. with respect to the production and sale of these auto parts, classify each cost as either variable costs, fixed costs, or mixed costs. 1. oil used in manufacturing equipment 2. plastic 3. property taxes, $165,000 per year on factory building and equipment 4. salary of plant manager 5. cost of labor for hourly workers 6. packaging 7. factory cleaning costs, $6,000 per month 8. metal 9. rent on warehouse, $10,000 per month plus $25 per square foot of storage used 10. property insurance premiums, $3,600 per month plus $0.01 for each dollar of property over $1,200,000 11. straight-line depreciation on the production equipment 12. hourly wages of machine operators 13. electricity costs, $0.20 per kilowatt-hour 14. computer chip (purchased from a vendor) 15. pension cost, $1.00 per employee hour on the job

Apharmaceutical packaging company (ppc) has decided to reorganize its processes into cells. the company has four different production operations, each requiring a unique piece of equipment. the names and functions of the four pieces of equipment are sort, count, place, and package. the company packages five different families of products (a, b, c, d, and e). the tables below indicate the demand (total units/day by product family), required operations, and operation cycle times for each product family. assume that any individual piece of equipment is available to operate 16 hours/day, but 2 hours (in total) are lost each day on each piece of equipment due to breaks and meetings when operators are not available to operate the equipment. how many minutes/day are available for production