Question 1 ( 4 points) Graves Lighting is planning this week's schedule for a metal stamping machine. It has been decided that they will make several models of exterior lanterns. All necessary accessories and glass inserts are in ample supolv. The number of RX188 should not exceed 40% of the total number of units produced. Also there should be at least two MX142 for every QX156 made. With the decision variables M,Q,R, and S respectively defined as the number of MX142, QX156, RX188, and SZ203 made, which of the following models represents a linear programming problem that will allow Graves to determine the number of a linear programming problem that will allow Graves to determine the number of each model to make such that profits are maximized. a) \[ \begin{array}{ll} \text { Maximize } & \text { Profit }=2.56 M+2.34 Q+3.09 R+2.74 S \\ \text { Subject to } & 1.2 M+1.3 Q+2.0 R+1.5 S \leq 2400 \\ & 2.4 M+1.9 Q+1.8 R+2.0 S \leq 3200 \\ & 1.0 M+1.0 Q+1.0 R+1.0 S \leq 1800 \\ & S \geq 500 \\ & R \leq 0.4(M+Q+S+R) \\ & \text { sve }-\varangle \psi \leq v \\ & M, Q, R, S \geq 0 \end{array} \] b) MaximizeSubjecttoProfit=2.56M+2.34Q+3.09R+2.74S1.2M+1.3Q+2.0R+1.5S24002.4M+1.9Q+1.8R+2.0S32001.0M+1.0Q+1.0R+1.0S1800S500R0.4(M+Q+S+R) KU.4(M+Q+S+K)M2Q0M,Q,R,S0 c) aximizeSubjecttod)MaximizeSubjecttorfit2.56.2.34Q,3.09.2.74S1.2M+1.3Q+2.0R+1.5S24002.4M+1.9Q+1.8R+2.0S32001.0M+1.0Q+1.0R+1.0S1800S500R0.4(M+Q+S+R)2MQ0M,Q,R,S0Profit=2.56M+2.34Q+3.09R+2.74S1.2M+1.3Q+2.0R+1.5S24002.4M+1.9Q+1.8R+2.0S32001.0M+1.0Q+1.0R+1.0S1800 d)MaximizeSubjecttoProfit=2.56M+2.34Q+3.09R+2.74S1.2M+1.3Q+2.0R+1.5S24002.4M+1.9Q+1.8R+2.0S32001.0M+1.0Q+1.0R+1.0S1800S500R0.4(M+Q+S+R)M2Q0M,Q,R,S0