Operations Research Answers

     Two different products P1 and P2 can be manufactured by one or both of two different machines M1 and M2. The unit processing time of either product on either machine is the same. The daily capacity of machine M1 is 200 units (of either P1 or P2 or a mixture of both) and the daily capacity of machine M2 is 250 units. The shop supervisor wants to balance the products schedule of the two machines such that the total number of units produced on one machine is within 5 units of the number produced on the other. The profit per unit of P1 is $10, and that of P1 is $15. Set up the problem as an LP in equation form.

A self-service photo centre allows you to make prints of pictures on an A4 size page. Two types of layouts

are available:

nnnnnlayout x: four pictures are fitted on one page, each has size 6 cm by 4 cm

nnnnnlayout y: two pictures are fitted on one page, each has size 15 cm by 9 cm

It costs R30 to print one page with layout x and it costs R40 to print one page with layout y.

You want at least 16 pictures of any size, and you are willing to spend up to R240. Write and graph a

system of inequalities that models the situation. Shade the solution space of the system of inequalities.

A hog raiser is mixing two types of grains A and B. each units of grain A costs P50 and contains 20 grams of fat and 10 grams of protein. Each unit of grain B costs P80 and contains 30 grams of fat and 30 grams of proteins. The hog raise wants each units of the final product to yield at least 180 grams of fat and at least 120 grams of protein. How many units of each type of grain should he use to maximize his sales?

A veterinarian mixes two types of animal food: Food 1 and Food 2. Each unit of Food 1 cost P200 and contains 40 grams of fat, 30 grams of protein, and 1, 200 calories. Each unit of Food 2 cost P180 and contains 40 grams of fat, 60 grams of protein, and 1,600 calories. Suppose the veterinarian wants each unit of the final product to yield at least 360 grams of fat, at least 240 grams of protein and at least 9, 600 calories, how many grams of each of type of ingredients should the veterinarian use to minimize his cost?

RB Music Store assembles stereo equipment for resale in the shop. The store offers two products; two products; turntables and cassette players. The store makes a profit of P400 on each turntable and P250 on each cassette. Both must go through two steps-assembly and bench checking. A turntable takes qw hours to assemble and 4 hours to bench check. A cassette player takes 4 hours to assemble but 8 hours to bench check. Looking at this month’s schedule, the store sees that it has 60 assembly hours uncommitted and 40 hours bench-cutting time available. What combination of turntables and cassette players would maximize the store’s profit for the month?