help. thanks. no exel please just a pencil and paper explanation. Use LINDO Digital Controls, Inc. $($DCI$),$ manufactures two models of a radar gun used by police to monitor the speed of automobiles. Model A has an accuracy of plus or minus $1$ mile per hour, whereas the smaller model B has an accuracy of plus or minus $3$ miles per hour. For the next week, the company has orders for $100$ units of model A and $150$ units of model B$.$ Although DCI purchases all the electronic components used in both models, the plastic cases for both models are manufactured at a DCI plant in Newark, New Jersey. Each model A case requires $4$ minutes of injection$-$molding time and $6$ minutes of assembly time. Each model B case requires $3$ minutes of injection$-$molding time and $8$ minutes of assembly time. For next week, the Newark plant has $600$ minutes of injection$-$molding time available and $1080$ minutes of assembly time available. The manufacturing cost is$ $10$ per case for model A and $ $6$ per case for model B$.$ Depending upon demand and the time available at the Newark plant, DCI occasionally purchases cases for one or both models from an outside supplier in order to fill customer orders that could not be filled otherwise. The purchase cost is $ $14$ for each model A case and $ $9$ for each model B case. Management wants to develop a minimum cost plan that will determine how many cases of each model should be produced at the Newark plant and how many cases of each model should be purchased. The following decision variables were used to formulate a linear programming model for this problem: A M$=$ number of cases of model A manufactured B M$=$ number of cases of model B manufactured A P$=$ number of cases of model A purchased B P$=$ number of cases of model B purchased The linear programming model that can be used to solve this problem is as follows:

$[$ Min $10$ A M$+6$ B M$+14$ A P$+9$ B P; S$.$t$.$; $1$ A M$+1$ A P$+=100$ Demand for model A; $1$ B M$+1$ B P$=150$ Demand for model B; $4$ A M$+3$ B M $<=60$ Injection molding time; $6$ A M$+8$ B M $<=1080$ Assembly time; A M$,$ B M$,$ A P$,$ B P $>=0$; $]$

The computer solution is shown in Figure $3\mathrm{.}18.$ a$.$ What is the optimal solution and what is the optimal value of the objective function? b$.$ Which constraints are binding? What are the dual values? Interpret each.