A local manufacturing firm produces four different metal products, each of which must be machined, polished and assembled. The specific time requirements (in hours) for each product are as follows:


Machining, hours
Polishing,hours
Assembling, hours

ProductI
3
1
2

ProductII
2
1
1

ProductIII
2
2
2

ProductIV
4
3
1


The firm has available to it on weekly basis,480 hours of machining time,400 hours ofpolishing time and 400 hours of assembling time.The unit profit son the product

are $ 360, $240, $360 and $ 480, respectively. The firm has a contract with a distributor to provide50unitsofproductI,and100unitsofanycombination of products II and III each week. Through other customers the firm can sell each week as many units of products I, II and III asitcanproduce,butonlyamaximum of 25 units of product IV. How many units of each product should the firm manufacture each week to meet all contractual obligations and maximize its total profit? Make a mathematical model for the given pro