Question

Constraints: a. We need 3,000 pounds of the mixture.

b. R₁ cannot be more than 900 pounds.
c. R₂ must equal 400 pounds.
d. R₃ cannot be less than 650 pounds.
e. R₄ must be at least 300 pounds. Find the combination of raw materials that will minimize cost.

Answer 1

The question involves optimizing a mixture of raw materials to meet a total weight with specific constraints on the quantities of each material. Calculations must consider the maximum for R₁, exact amount for R₂, minimum for R₃, and R₄ to reach the total of 3,000 pounds.

Step-by-step explanation:

The student's question pertains to combining raw materials to achieve a specific total weight while adhering to given constraints and minimizing cost. To find the optimal combination, the constraints must be carefully considered. For instance, if R₁ cannot be more than 900 pounds and R₂ must equal 400 pounds, this information along with the other constraints R₃ and R₄ will determine the weights of each component in the mixture. The goal is to meet the total weight of 3,000 pounds. This is a classic optimization problem that can be solved using techniques such as linear programming if costs are also given for each raw material.

To address constraint 'b' and 'c', and assuming the costs are directly related to the weight, we would use 900 pounds of R1, since it is the maximum allowed, and exactly 400 pounds of R2, since it must be exactly that amount. We would then make sure R3 is at least 650 pounds and R4 at least 300 pounds, increasing these amounts as needed to reach the total required weight of 3,000 pounds.