Use the case below to answer the following question(s).
S&N Manufacturing makes four different steel sheets,A,B,C,and D,with different percentages of iron.Each sheet must flow through five departments,forming,rolling,sintering,painting,and quality check.The table below shows the relevant data.Production rates are shown in units/hour.(Sheet A uses imported steel and does not require rolling.) S&N wants to determine the number of steel sheets to produce in order to maximize monthly profit.
Let A,B,C,and D denote the number of units of model A,B,C,and D to be produced,respectively.
-Which of the following is the inequality/equality that describes the time constraint of the painting department?
A)A/30 + B/30 + C/35 + D/25 ≤ 330
B)B/30 + C/20 + D/20 = 330
C)A/70 + B/50 + C/50 + D/44 = 330
D)A/60 + B/60 + C/70 + D/50 ≤ 330

Question

Use the case below to answer the following question(s).
S&N Manufacturing makes four different steel sheets,A,B,C,and D,with different percentages of iron.Each sheet must flow through five departments,forming,rolling,sintering,painting,and quality check.The table below shows the relevant data.Production rates are shown in units/hour.(Sheet A uses imported steel and does not require rolling.)   S&N wants to determine the number of steel sheets to produce in order to maximize monthly profit.
Let A,B,C,and D denote the number of units of model A,B,C,and D to be produced,respectively.
-Which of the following is the inequality/equality that describes the time constraint of the painting department?
A)A/30 + B/30 + C/35 + D/25 ≤ 330 
B)B/30 + C/20 + D/20 = 330 
C)A/70 + B/50 + C/50 + D/44 = 330 
D)A/60 + B/60 + C/70 + D/50 ≤ 330

Quizplus · Accepted Answer

The time constraint for the painting department is given by the inequality A/30 + B/30 + C/35 + D/25 ≤ 330, as shown in the table. To maximize monthly profit, we need to use linear programming techniques. Since there are four models and each model contributes differently to the profit, we need to define a profit function. Let P denote the profit per unit of each model. Then the monthly profit is given by Z = AP(A) + BP(B) + CP(C) + DP(D), where AP, BP, CP, and DP denote the production rates per hour for models A, B, C, and D, respectively. We also need to define the constraints for each department, as well as the non-negativity constraints for the production rates. Once we have set up the linear programming problem, we can use software or graphing techniques to find the optimal solution. The best choice(s) will depend on the specific values of the production rates and profits, but generally we would choose the production rates that maximize the profit subject to the constraints.

Use the Case Below to Answer the Following Question(s)