Asupermarket has been experiencing long lines during peak periods of the day. the problem is noticeably worse on certain days of the week, and the peak periods are sometimes different according to the day of the week. there are usually enough workers on the job to open all cash registers. the problem is knowing when to call some of the workers stocking shelves up to the front to work the checkout counters. how might decision models the supermarket? what data would be needed to develop these models?

Acompany manufactures x units of product a and y units of product b, on two machines, i and ii. it has been determined that the company will realize a profit of $3 on each unit of product a and $4 on each unit of product b. to manufacture a unit of product a requires 7 min on machine i and 5 min on machine ii. to manufacture a unit of product b requires 8 min on mchine i and 5 min on machine ii. there are 175 min available on machine i and 125 min available on machine ii in each work shift. how many units of a product should be produced in each shift to maximize the company's profit p?