Question

Your computer-supply store sells two types of inkjet printers. The first, type A, costs $237 and you make a $22 profit on each one. The second, type B, costs $122 and you make a $19 profit on each one. You can order no more than 120 printers this month, and you need to make at least $2,400 profit on them. If you must order at least one of each type of printer, how many of each type of printer should you order if you want to minimize your cost? Possible answers:
69 of type A : 51 of type B
40 of type A : 80 of type B
51 of type A : 69 of type B
80 of type A : 40 of type B
A factory can produce two products, x and y, with a profit approximated by P = 14x + 22y – 900. The production of y can exceed x by no more than 200 units. Moreover, production levels are limited by the formula x + 2y ≤ 1600. What production levels yield maximum profit?
x = 400; y = 600
x = 0; y = 0
x = 1,600; y = 0
x = 0; y = 200

Answer 1

The minimum cost option can be obtained simply by multiplying the number of ordered printers by the cost of one printer and adding the costs of both types of printers. Considering the options:
69 x 237 + 51 x 122 = 22,575
40 x 237 + 80 x 122 = 19,240
51 x 237 + 69 x 122 = 20,505
80 x 237 + 40 x 122 = 23,840
Therefore, the lowest cost option is to buy 40 of printer A and 80 of printer B

The equation, x + 2y ≤ 1600 is satisfied only by options:
x = 400; y = 600
x = 1600
Substituting these into the profit equation:
14(400) + 22(600) - 900 = 17,900
14(1600) + 22(0) - 900 = 21,500
Therefore, the option (1,600 , 0) will produce greatest profit.