Question 1: (20 marks) SDS, a private higher education institution which mission is to become a leader in social contribution, nurtures two important types of talents, SCM and MSIM, for the better future development of the society with three crucial resources: Care, Guidance and Support. The following table shows the resources requirements for a unit of talent output and the resource capacities of SDS currently available. RESOURCES Care Guidance Support TYPES OF TALENTS SCM MSIM 6 4 2 2 2 1 RESOURCE CAPACITIES 48 18 16 The social contribution per unit output of SCM and MSIM are 40 and 34, respectively. Linearity is assumed in this problem. (a) Formulate this problem as a linear program. (3 marks) (8 marks) (b) Use the Corner-Point Method to find the optimal solution of the problem. (c) If SDS wants to increase its social contribution by increasing its outputs of SCM and MSIM, which resource(s) should be acquired or purchased? (3 marks) (d) What is the unit price (in terms of social contribution) SDS should pay for each additional unit of the acquired resource identified in (c)? (6 marks) (TOTAL 20 MARKS)