(b) To fill an order for 100 units of a product, a firm wishes to distribute the production between its two plants, Plant 1 and Plant 2. The total cost function is given by
c=f(q_1,q_2 )=0.5q_1^2+2q_1+32q_2+500
where q_1 and q_2 are the number of units produced at Plants 1 and 2, respectively. How should the output be distributed in order to minimize costs?
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