8. John has been in the habit of mowing Willa's lawn each week for $20. John's opportunity cost is $15, and Willa would be willing to pay $25 to have her lawn mowed. What is the maximum tax the government can impose on lawn mowing without discouraging John and Willa from continuing their mutually beneficial arrangement

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?