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?

Question

A. 69 of type A : 51 of type B
B. 40 of type A : 80 of type B
C. 51 of type A : 69 of type B
D. 80 of type A : 40 of type B

Answer 1

Let's first assign variables to the number of printers of each type we will order. Let x denote the number of type A printers and y denote the number of type B printers.

Since we must order at least one of each type, we know that x > 0 and y > 0.

Now let's set up the constraints based on the given information:
1) x + y ≤ 120 (We can order no more than 120 printers.)
2) 22x + 19y ≥ 2400 (We need to make at least $2,400 profit on the printers.)

To minimize the cost, we need to minimize the total cost function C(x, y), which is given by:
C(x, y) = 237x + 122y

To solve this linear program, we can use a graphical method or a mathematical method called linear programming. Here, we will use the graphical method.

First, we will plot the feasible region on a graph based on the constraints.

For constraint 1: x + y ≤ 120
We can rewrite this constraint as y ≤ -x + 120 and plot the corresponding line on the graph.

Now, we will plot the other constraint on the same graph.
For constraint 2: 22x + 19y ≥ 2400
We can rewrite this constraint as y ≥ (-22/19)x + (2400/19) and plot the corresponding line on the graph.

The graph will show the feasible region, and the point at which the total cost function C(x, y) has the minimum value will give us the optimal solution.

After plotting the feasible region, we see that the coordinates that minimize the cost fall between the points (51, 69) and (69, 51).

Therefore, the answer is option A: 69 of type A and 51 of type B.