Scenario III: Goodmark Company produces two types of birthday cards: scented and regular. During the year, 20,000 scented cards and 200,000 regular cards were produced. Goodmark has two production departments: Cutting and Printing. Direct labor hours are used to assign the overhead of Cutting and machine hours are used for Printing. The data for the two producing departments are given below:

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?