Q$1$:Prepare mix design for given data;

$$The$28-$day compressive strength should be $4000$ psi,The slump should be between $75$mm and $100$mm and the maximum aggregate size should not exceed $19$mm$.$The properties of the materials are as follows:

$$Cement: Type I, specific gravity$=3\mathrm{.}15$

$$Coarse Aggregate:

Bulk specific gravity$=2\mathrm{.}64$; absorption capacity$=0\mathrm{.}45\%$; dry$-$rodded unit weight$=1612$kg$/$m$3,$ surface moisture$=1\mathrm{.}05\%$

$$Fine Aggregate:

Bulk specific gravity$=2\mathrm{.}67$; absorption capacity$=1\mathrm{.}15\%$; fineness modulus$=2\mathrm{.}80$;surface moisture$=3\mathrm{.}13\%$