Let's denote the number of type A printers as "a" and the number of type B printers as "b".
From the condition, we know that a + b ≤ 120 (we can order no more than 120 printers).
The profit from type A printers is 22a, and the profit from type B printers is 19b. We need to make at least $2,400 profit, so the inequality is 22a + 19b ≥ 2,400.
We also know that a ≥ 1 (we must order at least one type A printer) and b ≥ 1 (we must order at least one type B printer).
To minimize the cost, we need to minimize the total cost, which is the sum of the costs of the type A and type B printers.
The cost of type A printers is $237a, and the cost of type B printers is $122b.
Therefore, the objective function is: Cost = 237a + 122b.
We can use linear programming to solve this problem.
Subject to:
a + b ≤ 120
22a + 19b ≥ 2,400
a ≥ 1
b ≥ 1
Minimize:
Cost = 237a + 122b
Solving this linear programming problem will give us the optimal values for "a" and "b", telling us how many of each type of printer we should order to minimize the cost while meeting the profit requirement.
Your computer-supply sore cells 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?
1 answer