Wear ever is expanding and needs $6.8 million to fund this growth. the company estimates it can sell new shares of stock for $43 a share. it also estimates it will cost an additional $352,000 for filing and legal fees related to the stock issue. the underwriters have agreed to a spread of 7.5 percent. how many shares of stock must be sold for the company to fund its expansion?

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?