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?(1 point)Responses69 of type A : 51 of type B69 of type A : 51 of type B40 of type A : 80 of type B40 of type A : 80 of type B51 of type A : 69 of type B51 of type A : 69 of type B80 of type A : 40 o
f type B
To solve this problem, we can use a system of linear equations.
Let's assume we order x printers of type A and y printers of type B.
The cost equation for the printers is:
237x + 122y = Total Cost
The profit equation for the printers is:
22x + 19y = Total Profit
We know that we need to make at least $2,400 profit, so the profit equation can be rearranged to:
22x + 19y ≥ 2400
We also know that we can order no more than 120 printers, so the total number of printers equation is:
x + y ≤ 120
Since we need to order at least one of each type of printer, we can add the constraint:
x ≥ 1
y ≥ 1
To minimize the cost, we can use linear programming techniques to find the feasible region and the optimal solution.
Solving these equations and constraints will give us the answer. I will calculate it for you.
Please wait a moment while I find the solution.
To minimize your cost while meeting the given constraints, you can solve this problem using linear programming. Here's how you can approach it step-by-step:
1. Define the variables: Let's say you order x printers of type A and y printers of type B.
2. Write the objective function: The objective is to minimize the total cost, which can be calculated by multiplying the number of printers by their respective costs and then subtracting the profit. So the objective function becomes:
Cost = 237x + 122y - 22x - 19y
3. Write the constraints:
- The total number of printers ordered should not exceed 120:
x + y ≤ 120
- The minimum profit requirement should be met:
(22x + 19y) ≥ 2400
- The minimum quantity requirement of at least one printer of each type:
x ≥ 1
y ≥ 1
4. Solve the linear programming problem: Use a graphing calculator, software, or an online tool (such as WolframAlpha or Excel Solver) to find the optimal solution.
The optimal solution, which minimizes the cost while satisfying the given constraints, is:
69 of type A printers and 51 of type B printers.
Therefore, the correct response is:
69 of type A : 51 of type B.